homeless vs bag lady

homeless and bag lady both are nouns.

Word	Noun	Adjective	Verb	Adverb
homeless	Yes	Yes	No	No
bag lady	Yes	No	No	No

As nouns, bag lady is a hyponym of homeless; that is, bag lady is a word with a more specific, narrower meaning than homeless:

homeless: someone unfortunate without housing
bag lady: a homeless woman who carries all her possessions with her in shopping bags

homeless (noun)	bag lady (noun)
poor people who unfortunately do not have a home to live in	a homeless woman who carries all her possessions with her in shopping bags
someone unfortunate without housing

homeless (adjective)	bag lady (adjective)
physically or spiritually homeless or deprived of security
without nationality or citizenship