'Umrah in Ramadhan is equal to a Hajj
Question :
Are there any Hadiths reported that prove that 'Umrah in Ramadhan is equal to a Hajj or that its virtue is just like the other months?
Answer:
Yes, it is reported in Sahih Muslim from the Prophet ﷺ that he said:
"An 'Umrah in Ramadhan is equal to a Hajj."
So 'Umrah performed in Ramadhan is equal to a Hajj, just as the Hadith has mentioned. However, this does not mean that it suffices for the performance of Hajj, such that if a person made Umrah in Ramadhan and he did not perform the obligation of Hajj, he does not have to perform the obligatory Hajj. This is because the equivalency of one thing to another does not necessitate that one suffices in place of the other.
Hence, this Surah (chapter of the Qur'an): "Say: He is Allâh (the) One," is equal to a third of the Qur'an. However, it does not suffice in place of it. So, if someone repeated Suratul-Ikhlas three times in his prayer, that does not suffice him in place of reciting Suratul-Fatihah. Also, this saying of a person: "There is none worthy of being worshiped as a God except Allâh alone. To Him belongs the sovereignty and to Him belongs the praise, and He has power over all things." The person saying this ten times is like whoever freed four souls (people) from the children of Isma'il. However, with this, if a person said this and upon him is the obligation of freeing a slave, this saying does not suffice in its place. By this you know that something being comparatively equal to something else does not necessitate that it suffices in place of that thing.
Source:
Ash-Shaykh Ibn 'Uthaimin
Fatawa Islamiyah, Vol. 4 Pages 292-293