I have noted that the Shia Muslims use a stone called (Muhr) for saying prayers but the Sunni Muslims don't use that and also consider it something taboo.
Why such difference in style?
Both Shia and Sunni scholars allow prostration over clay, stone and alike materials beside many other materials, but there are some materials that are not allowed for Shia brothers to prostrate over it, like the carpets, that Sunni brothers know as allowable to be used for prostration. Among all those materials that is allowed for Shia brothers to prostrate over the clay is the best encouraged material and if the clay is from Karbala that would be the best of bests. However, as nowadays in the cities and in the apartments and buildings not everywhere on the floor is allowed to prostrate over it according to Shia Fiqh, it is very common among the Shia Muslims that everyone has a piece of stone or clay in his house, in places for prayers in shopping centers and etc, in shrines and in the mosques. Also as clay is preferred over the stones so this is even a better reason to use a piece of clay everywhere even if the floor is covered with stone or other allowable materials. None of these is wrong in the Sunni view as well, but the problem is that as the piece of clay or stone is placed at the prostration point a head of the person while praying, some may think that the person is praying in front of a stone toward that stone, like worshiping the idols, but this is only a misconception of what the Shia brothers are doing. The piece of clay or stone is only to be used as a place for the forehead to rest over it while being in prostration, not as an idol or else.
According to Jafari Fiqh sujud (prostration) should be only on earth and if is on other things like carpet the prayer is not accepted. Shia Muslims use anything that is considered part of earth like a stone or Muhr (made by soil) for genuflection.
(Some Sunni Muslims think Shia worship to stone itself as idol and so consider it as polytheism and taboo. Using a stone among Shia is similar to praying towards Kabba which isnot worshiping Kaaba itself.)
Imam Sadiq S.A. always had emphasized this. Here are some hadith from Sunni hadith books:
Abu Said Al Khudri narrates:
The Messenger of Allah used to practice Itikaf (in the mosque), in the middle third of Ramadan. After the twentieth night, he used to return home on the twenty-first, and those who were in Itikaf with him would return to their homes as well. In Ramadan, in which he practiced Itikaf, he would pray the night prayers on the night in which he returned home, and then address the people, instructing them as Allah commanded him. He said, "I used to practice Itikaf for these ten days (i.e. the middle third of Ramadan), but I now intend to stay in Itikaf for the last ten days. Whoever was in Itikaf with me should stay at his place of seclusion. I have certainly been shown (the date of) this Night (of Qadr), but I have forgotten it. Search for it in the odd nights of the last ten days (of Ramadan). I also saw myself (in a dream) prostrating in mud and water." On the twenty-first night, the sky was covered with clouds and it rained, and the rainwater started leaking through the roof of the mosque onto the praying place of the Prophet. With my own eyes, I saw the Prophet, upon completion of the morning prayer, leaving (the mosque) with his face covered with mud and water.
Sahih Al-Bukhari Hadith 3.235
Abu Hazim narrates:
Sahl bin Sa'd was asked about the (Prophet's) pulpit, as to what was it made of. Sahl replied: No one is still alive among the people who knows about it better than I. It was made of tamarisk forest wood. So and so, the slave of so and so, prepared it for the Messenger of Allah. When it was constructed and placed (in the mosque), the Messenger of Allah stood on it, facing the Qibla, and said, "Allahu Akbar", and the people stood behind him (in prayer). He recited and bowed, and the people behind him bowed. Then he raised his head, stepped back, descended and prostrated on the ground. He then again ascended the pulpit, recited, bowed, raised his head, stepped back, descended and prostrated on the ground. This is what I know about the pulpit.
Sahih Al-Bukhari Hadith 1.374
Hazrat Maimuna said:
The Messenger of Allah used to pray on a Khumra (a palm leaf mat large enough to place one's face, while in prostration).
Sahih Al-Bukhari Hadith 1.378
Jabir bin Abdullah narrates:
The Messenger of Allah said: I have been given five things which were not given to any of the Prophets before me. These are:
Sahih Al-Bukhari Hadith 1.429
Abu Sa'eed used to relate that he had seen the Prophet prostrating on wet mud, so much so that he could see mud stains on his forehead.
Saheeh Bukhari, Part I, p. 104
Hazrat Maimuna said:
The Messenger of Allah was once praying while I was experiencing my menses and sitting beside him. Sometimes his clothing would touch me during his prostration. She added: He prayed on a Khumra (a small palm leaf mat).
Saheeh Bukhari, Volume 1, Book 8, Number 376
The Prophet used to place his forehead on the earth while prostrating.
Saheeh Bukhari, Part 1, p. 97
The Prophet declared that the best place for prostration was the earth, or upon something that grows from the earth.
Kanz-ul-Ummal, Part 4., p. 113 (Famous Sunni book of Hadith)
The Prophet said to his wife Umm Salma, " Bring me the Khumra from the mosque." The word Khumra means a small piece of chatai made from palm leaf, on which only the head could be rested when prostrating. lbn-Athir, in his Jami-al-Usool has written, "Khumra is the Sajdagah (Persian word meaning "prostration place") upon which the Shias of our time perform their prostrations."
I (i.e. Maulana Zamankhan) maintain that by this Hadith it is Sunnat to keep a Sajdagah. Those who forbid it and call it the way of the Rafizites (Shiites) are wrong. To practice this Sunnat, I often perform my prostrations on a fan made from palm leaf, and I do not care about the criticism of the ignorant. We are concerned only with the Sunnat of the Prophet (SAA), regardless of whether they call it the way of the Rafizites or the Kharijites. Let them rave about it.
Maulana Vahidul Zamankhan (Sunni Alim), author of 'Anwar-ul-Lughat', Chap. 7, p. 118
Why the Asr prayer may be prayed immediately after Zuhr, and the Isha prayer immediately after Maghrib
It is narrated on the authority of Ibn Abbas, that he said that the Messenger of Allah prayed Zuhr and Asr together, and also Maghrib and Isha, although he was neither in a state of fear nor on a journey.
Saheeh Muslim, Vol. I, p.264
Ibn Abbas narrates that the Messenger of Allah recited the Zuhr and Asr prayers together, and also said the Maghrib and Isha prayers, although he was neither in a state of fear, nor was there any other cause, e.g. rain. It is related from Waki that he asked Ibn Abbas the reason (for the joint prayers). Ibn Abbas replied: So that the followers (of the Prophet) may not experience inconvenience and difficulty.
(1) Saheeh Muslim, Vol. I, p.265 (2) Jami Tirmizee, p. 54
Abdullah Bin Shaqeeq narrates that one day after the Asr prayer, Ibn Abbas began delivering a sermon which was so long that the sun set and the stars appeared. People began to shout: Salat! Salat! (as it was time for Maghrib prayer). Ibn Abbas paid no heed to them until someone from Bani Tameem stood up and shouted continously: Salat! Salat! Ibn Abbas responded: Woe unto you! You wish to teach me the Sunnat? He said: I have personally seen the Messenger of Allah pray the Zuhr and Asr prayers together, and likewise, the Maghrib and Isha prayers.
The narrator says: This statement of Ibn Abbas kept disturbing my conscience until I went and asked Abu Huraira about it, and he attested to what Ibn Abbas had said.
Saheeh Muslim, Vol. 1 p. 265
It is related from Ibn Abbas that the Prophet at one time recited seven rakats of prayers, and at another time eight rakats, i.e. he recited the Maghrib and Isha prayers together, and the Zuhr and Asr prayers together.
Saheeh Bukhari, Part I, p.72
It is narrated by Ibn Abbas that in Madina the Prophet used to recite two prayers together (Zuhr and Asr, and Maghrib and Isha), without there being any fear or rainfall. When asked about the reason for this, he said: The Prophet desired that his followers may not suffer inconvenience, and therefore the two prayers may be recited together.
one shia Hadith:
قال هشام بن الحكم لابي عبدالله عليه السلام: " أخبرني عما يجوز السجود عليه وعما لا يجوز؟ قال: السجود لا يجوز إلا على الارض أو على ما أنبتت الارض إلا ما أكل أو لبس فقال له: جعلت فداك ما العلة في ذلك؟ قال: لان السجود خضوع لله عزوجل فلا ينبغي أن يكون على ما يؤكل أو يلبس لان أبناء الدنيا عبيد ما يأكلون ويلبسون، والساجد في سجوده في عبادة الله عزوجل فلا ينبغي أن يضع جبهته في سجوده على معبود أبناء الدنيا الذين اغتروا بغرورها، والسجود على الارض أفضل لانه أبلغ في التواضع والخضوع لله عزوجل "
Hisham b. al-Hakam said to Abu
The sunni's don't use a stone (Muhr) as the shia because there is no hadith from the prophet (PBUH) that says we should only pray on a stone. On the contrary, Islam is an easy religion to its followers and not to ask them to do things that they will not be able to do such as we should only pray on a stone.
In the Quran:
However, We have a hadiths (in Sahih Bukhary and Sahih Muslim) that says we can pray on anything we want.
Jabir b. 'Abdullah al-Ansari reported:
The Prophet (may peace be upon him) said:
Narrated Maimuna: (the wife of the Prophet)
(In Bukhary and Muslim)
NOTE : The two points that Ahmad has mentioned above in the "short answer part" which are:
1 - sunnis are OK with using a clay/stone"
2 - sunnis think "some may think that the person is praying in front of a stone toward that stone, like worshiping the idols, but this is only a misconception of what the Shia brothers are doing"
This is blatantly wrong!!!
Sunnis are not OK with someone praying on a clay/stone because there is no hadith says we should. So if someone does that he is inventing something new is Islam aka Bida'ah.
As for the 2nd point, sunnis don't think praying on a stone is considered worshiping idols. I don't know how did you come up with this. There is no fatwa or anything that says so. If there is please provide an evidence.
However, sunnis have a problem with shia when it comes to using a clay from Karbala(where Hussien is buried). Sunnis say why don't shia use a clay from Madina or Mecca ? Isn't it billion times better than karbala ? which shows how bad this is when you think there is a holier place othan than Meccah or Madinah
The only material we pray on is mud that is pure and clean. We don't pray on clay to "worship it", we pray on it because it is pure, and as all Muslims — Shi'a and Sunni — believe that one must be clean and in a clean environment to pray.
I once asked my Sunni friend: "Why do you Sunni people pray with your shoes on in the mosque? Isn't the mosque an untainted and a holy place? What if you get mud on shoes, can you still pray with them?" She replied with: "Yes we can pray with our shoes if there's mud on it because mud is 'tahr' so it doesn't really matter" I told her that "Us Shi'a Muslims pray on mud merely because its 'tahr' and Sunni Muslims object that and believe that we are worshiping them as idols"
The point is that us Shi'a Muslims pray on a 'turbah' (which comes from the word tarab that means mud) because it is tahr and pure. And the prophet used to pray on pure flat GROUND because in the prophet's time they did not have a sijadah as there was no technology back then to produce them.