What are the differences between these three types of Hajj: Mofrad, Mokren, and Motamatte3?
I know the difference is concerning Ihram, but what is exactly each one of them?
There are three types =
Hajj Mofrad is when one enters into the state of Ihram for Hajj only and no Umrah is performed before Hajj.
Hajj Tamattu is when the pilgrim removes Ihram for Umrah on the 8th of Thul-Hijjah and re-enters into the state of Ihram again for Hajj. Umrah is done before Hajj.
Hajj Qiran is when a pilgrim enters into the state of Ihram for both Umrah and the Hajj.
In the qur'an hajj is often quoted beside 'umrah. So both kinds of pilgrimage are clearly mentioned and have a backup in the qur'an itself. The major difference between both is that hajj can only be performed in a specific time in specific days in the year (see 2:197 and Why Quran use 'Months' for period of Hajj?) while 'umrah can basically be performed at anytime and that hajj is obligatory if one can afford it based on (3:97)
... And [due] to Allah from the people is a pilgrimage to the House - for whoever is able to find thereto a way. ...
Scholars have based on that and based on the practice (sunnah) of the Prophet() defined three types or forms of hajj:
Verse (2:196) covers the qiraan and tamattu' forms according some scholars:
And complete the Hajj and 'umrah for Allah . But if you are prevented, then [offer] what can be obtained with ease of sacrificial animals. And do not shave your heads until the sacrificial animal has reached its place of slaughter. And whoever among you is ill or has an ailment of the head [making shaving necessary must offer] a ransom of fasting [three days] or charity or sacrifice. And when you are secure, then whoever performs 'umrah [during the Hajj months] followed by Hajj [offers] what can be obtained with ease of sacrificial animals. And whoever cannot find [or afford such an animal] - then a fast of three days during Hajj and of seven when you have returned [home]. Those are ten complete [days]. This is for those whose family is not in the area of al-Masjid al-Haram. And fear Allah and know that Allah is severe in penalty.
some conclude from it that qiraan is recommended for those who come from far away!
All three kinds are covered in the hadith:
We set out with Allah's Messenger (ﷺ)s (to Mecca) in the year of the Prophet's Last Hajj. Some of us had assumed Ihram for 'Umra only, some for both Hajj and 'Umra, and others for Hajj only. Allah's Apostle assumed Ihram for Hajj. So whoever had assumed Ihram for Hajj or for both Hajj and 'Umra did not finish the Ihram till the day of sacrifice.
(Sahih al-Bukhari, sahih Muslim, Muwatta' Malik and others)
In the version of an-Nasa'i 'Aisha added:
"And I was one of those who had entered Ihram for Umrah."
A helpful source in Arabic.