illegitimately vs out of wedlock

illegitimately and out of wedlock both are adverbs.

Word	Noun	Adjective	Verb	Adverb
illegitimately	No	No	No	Yes
out of wedlock	No	No	No	Yes

As adverbs, illegitimately and out of wedlock are synonyms defined as:

illegitimately and out of wedlock: of biological parents not married to each other

illegitimately (adverb)	out of wedlock (adverb)
of biological parents not married to each other	of biological parents not married to each other
in a manner disapproved or not allowed by custom	of unwed parents