All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The greater Hajj is Hajj itself and the minor Hajj is ‘Umrah according to the view of the majority of the scholars . Ibn Hajar said: “The scholars differed in opinion in regard to what is meant by the minor Hajj, and the majority of them are of the view that it is ‘Umrah. It was also said that the minor Hajj is the day of ‘Arafah and the greater Hajj is the day of Al-Adh-ha [i.e. the day of ‘Eed] as on this day the remaining rituals (of Hajj) are completed…”
The scholars named ‘Umrah the minor Hajj because of the letter of the Prophet to ‘Amr Ibn Hazm which reads “‘Umrah is the minor Hajj”.
Besides, the difference between Hajj and ‘Umrah is obvious: ‘Umrah is assuming the state of Ihraam, performing Tawaaf (circumambulation around the Ka’bah) and Sa’y, and shaving or trimming the hair, whereas Hajj has additional pillars and obligations, like standing at ‘Arafah, performing Tawaaf Al-Ifaadhah, staying overnight in Mina and Muzdalifah, throwing the stones and Tawaaf Al-Wadaa' (Farewell Tawaaf).
Therefore, having known that the greater Hajj is Hajj itself unlike the minor Hajj which is ‘Umrah, you should know that there is no relation between Friday and naming Hajj the greater Hajj, because Hajj is the greater Hajj whether or not the day of ‘Arafah coincides with Friday. Al-Mubaarak Poori said: “Note: It is widespread among the common people that if the day of ‘Arafah coincides with Friday then the Hajj is a greater Hajj, indeed, there is no evidence for this.”
Allaah Knows best.