Gfyuki

The definition of clitic seems to encompass
that of contractions. Is there a distinction?

[A clitic] is a word that is treated in pronunciation as forming a part of a neighboring word and that is often unaccented or contracted

-[Merriam Webster online]

These words have been used in various ways, but they are not synonymous.

"Contraction" can refer to various kinds of "shortenings", either in spoken language or in writing. Written contractions in English typically contain an apostrophe (although spellings like gonna and wanna might also be categorized as contractions). Sometimes a "contraction" might occur within a word: e.g. the full spelling probably could be replaced in writing with the "contraction" prob'ly to represent a common "contracted" pronunciation of this word. This last kind of "contraction" has nothing to do with clitics.

The definition of "clitic" is more problematic because it is a word that has been used in more technical contexts, but with a certain amount of vagueness or ambiguity. It can be roughly defined as something that acts like a "word" syntactically but not "phonologically". The most obvious examples of clitics in English are the contracted forms of auxiliary verbs such as 'm, 's, 've, 'll, 'd. The English possessive 's that can be found at the end of a noun phrase in contexts like "The Queen of England's dogs" has also been called a clitic; it is probably an example of a clitic that is not a contraction (there is no "uncontracted" form in modern English, and my understanding is that the most widely accepted etymology of the possessive 's is from an Old English suffix, so it didn't originate historically from "contracting" another word like his with a preceding noun).

An "enclitic" is a clitic that is phonologically dependent on the preceding word; the examples above are all enclitics. A clitic that is phonologically dependent on the following word is called a "proclitic": it has been argued that the pronominal agreement markers on French verbs are proclitics (example: le meaning "it" in je le ferai "I will do it").

The negative n't that appears in words like don't, won't, can't is commonly called a contraction, but it has been argued that it is a suffix and not a clitic (Zwicky and Pullum 1983). There is much more literature that builds on or responds to the discussion of the meaning of "clitic" in that paper, but I don't know enough about it to summarize it here.