advocate vs suggest

advocate is a noun but suggest is not a noun.

Word	Noun	Adjective	Verb	Adverb
advocate	Yes	No	Yes	No
suggest	No	No	Yes	No

As verbs, suggest is a hypernym of advocate; that is, suggest is a word with a broader meaning than advocate:

Other hypernyms of advocate include advise, propose.

advocate (noun)	suggest (noun)
a person who pleads for a cause or propounds an idea
a lawyer who pleads cases in court

advocate (verb)	suggest (verb)
push for something	make a proposal, declare a plan for something
speak, plead, or argue in favor of	call to mind
	imply as a possibility
	drop a hint; intimate by a hint