The Hajj is the pilgrimage to Mecca that culminates during Dhu al-Hijjah, near Eid al-Adha.
Hajj is one of the Five Pillars of Islam and is required once in a lifetime for Muslims who are physically and financially able to undertake it. Its major rites take place in and around Mecca, including standing at Arafat, spending time at Muzdalifah, and the stoning ritual at Mina.
Eid al-Adha falls on 10 Dhu al-Hijjah, during the annual Hajj season. The pilgrimage itself continues across several days, so Eid is closely connected with Hajj but is not identical to it.
Umrah is a separate pilgrimage that can be performed at other times of year, including Ramadan. This distinction is a common source of confusion when comparing the two journeys to Mecca.