hajj vs pilgrim's journey

hajj and pilgrim's journey both are nouns.

Word	Noun	Adjective	Verb	Adverb
hajj	Yes	No	No	No
pilgrim's journey	Yes	No	No	No

As nouns, pilgrim's journey is a hypernym of hajj; that is, pilgrim's journey is a word with a broader meaning than hajj:

hajj: 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
pilgrim's journey: a journey to a sacred place

Other hypernyms of hajj include pilgrimage, pillar of Islam.

hajj (noun)	pilgrim's journey (noun)
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	a journey to a sacred place