I've always been asked by my elders to sit down and then drink water. Why is it so and why doesn't the same rule apply while drinking Zam Zam.
Assalaamu alaikum warehmatullahi wabarakatuhu, The answer is, mostly it is due to the sunnah of our Prophet Muhammed SAW as stated in hadith he used to do so:
Volume 7, Book 69, Number 519 :
Narrated An-Nazzal: All came to the gate of the courtyard (of the Mosque) and drank (water) while he was standing and said, "Some people dislike to drink while standing, but I saw the Prophet doing (drinking water) as you have seen me doing now."
Sayyidina Anas ibn Malik radiyallahu anhu relates that Rasoolullah sallallahu alaihe wasallam drank water in three breaths (i.e. in three gulps/sips) and used to say, “It is more pleasing and satisfying in this manner.
Volume 7, Book 69, Number 521 :
Narrated by Ibn 'Abbas The Prophet drank Zam-Zam (water) while standing.
Volume 7, Book 69, Number 530 :
Narrated by Abu Said Al-Khudri I heard Allah's Apostle forbidding the drinking of water by bending the mouths of water skins, i.e., drinking from the mouths directly.
Note:- Say bismillah before drinking by taking 3 sips (not in the utensil) and Alhamdulillah after. As for Zam Zam, you pay respect to the holy water by standing and drinking it!
Is drinking whilst sitting sunna?
First of all it's permissible to drink both sitting and standing, but drinking whilst sitting is better, and it is what the Messenger of Allah (blessings and peace of Allah be upon him) did most often as even later people thought only this was his sunna. I will add references later!
Is drinking zam-zam whilst standing sunna?
The Hadith of ibn 'Abas saying that our Messenger (blessings and peace of Allah be upon him) drunk zam-zam whilst standing (Quoted by Imam al-Bukahri, Muslim, Ibn Majah etc.) is considered by some Scholars as a permission not a must, as in an other Narration a sub-narrator added that the Prophet (peace be upon him) was riding! So even while drinking zam-zam you could (should) sit, as this is the the position our Messenger (peace be upon him) toke the most for drinking!
References about the permission to drink whilst standing
Here are some ahadith references showing that the Messenger of Allah also has been seen drinking whilst standing (not only zam-zam).
From sahih al-Bukahri narrated by an-Nazzal (may Allah be pleased with him)
From Jami' at-Tirmidhi (and also in Sunan ibn Majah) narrated by ibn 'Omar (may Allah be pleased with both of them)
And in Musnad Ahmad:
‘Ali ibn Abi Taalib (may Allaah be pleased with him) drank whilst standing, and the people looked at him as if they objected to that. He said: “What are you looking at? If I drink whilst standing, I saw the Prophet (peace and blessings of Allaah be upon him) drink whilst standing, and if I drink sitting, I saw the Prophet (peace and blessings of Allaah be upon him) drink whilst sitting.”
And Allah knows best