They are usually not only synonymous but interchangeable (with,
perhaps, a modification in form).
A. What specifically did you not like about the movie?
B. What in particular did you not like about the movie?
Both of these mean that the listener should give details about what
they didn't like about the movie. No difference in meaning or nuance as
far as I can see.
C. He's very particular about the style of shoes he wears.
D. He's very specific about the style of shoes he wears.
These two usages are different.
Sentence C means that he's very fussy and choosy and won't wear a style
that he doesn't like, but he doesn't restrict himself to two or three
sentence D means that he will wear only a limited number of styles, and
that when he goes to a shoe store, he tells the salesman exactly
(specifically) what styles he's interested in buying, and nothing else