specially vs peculiarly

specially and peculiarly both are adverbs.

Word	Noun	Adjective	Verb	Adverb
specially	No	No	No	Yes
peculiarly	No	No	No	Yes

As adverbs, specially and peculiarly are synonyms defined as:

specially and peculiarly: to a distinctly greater extent or degree than is common

Other synonyms of specially include especially, particularly.

specially (adverb)	peculiarly (adverb)
to a distinctly greater extent or degree than is common	in a manner differing from the usual or expected
in a special manner	uniquely or characteristically
	to a distinctly greater extent or degree than is common