pillar of Islam vs haj

pillar of Islam and haj both are nouns.

Word	Noun	Adjective	Verb	Adverb
pillar of Islam	Yes	No	No	No
haj	Yes	No	No	No

As nouns, haj is a hyponym of pillar of Islam; that is, haj is a word with a more specific, narrower meaning than pillar of Islam:

pillar of Islam: (Islam) one of the five religious obligations accepted by all Muslims
haj: the fifth pillar of Islam is a pilgrimage to Mecca during the month of Dhu al-Hijja; at least once in a lifetime a Muslim is expected to make a religious journey to Mecca and the Kaaba

Other hyponyms of pillar of Islam include shahadah, salaah, salaat, salah, salat, sawm, zakat, hadj, hajj.

pillar of Islam (noun)	haj (noun)
(Islam) one of the five religious obligations accepted by all Muslims	the fifth pillar of Islam is a pilgrimage to Mecca during the month of Dhu al-Hijja; at least once in a lifetime a Muslim is expected to make a religious journey to Mecca and the Kaaba