A contraction is a combination of two lexemes, each of which maintains its own meaning.
Example: hasn’t ‘has not’
Contractions are different from compounds. A compound, such as ‘hasbeen’, is a combination of two lexemes with an unpredictable change in meaning. There is no such change in meaning in a contraction.
Contractions are different from clitics. A clitic is a lexeme that is grammatically independent but attaches phonologically to any adjacent word. An example of a clitic is the English possessive –’s in the phrases ‘Elizabeth’s hat’, ‘the queen’s hat’, and ‘the queen of England’s hat’. The clitic –’s obligatorily attaches to whatever word precedes it. In contrast a contraction is a specific pair of words that regularly combines. The combination may be obligatory, as in the case of ‘let’s’, as in “Let’s go” (“Let us go” has a different meaning), or it may be optional, as in the case of ‘we’ve’, as in “We’ve been honored,” or “We have been honored.”
Contractions are different from portmanteau morphemes. A portmanteau morpheme is a single, indivisible morpheme that combines two meanings that are usually expressed by separate morphemes. An example of a portmanteau morpheme is the word ‘were’ which is a single morpheme expressing the meaning of the lexeme ‘be’ and the grammatical category ‘Past.tense’. ‘Were’ cannot be divided into two morphemes. (Note that ‘busted’ can be divided into bust-ed ‘bust-Past.tense’.) In contrast the contraction ‘we’re’ (we are) can be divided into ‘we-’re’.
One or both members of a contraction can be shortened. Most English contractions only shorten the second member, as in ‘I’m’ (I am), ‘it’s’ (it is), ‘isn’t’ (is not). Others shorten both members, as in ‘won’t’ (will not), ‘shan’t’ (shall not), ‘ain’t’ (am not).
A contraction can combine more than two members, as in ‘wouldn’t’ve’ (would not have).
English orthography uses the apostrophe to indicate the loss of a phoneme, as in ‘shouldn’t’ (should not). But when both words lose a phoneme, only one apostrophe is used, as in ‘shan’t’ (shall not). In writing sometimes a contraction is written out as two separate words, even when it would normally be shortened to the contracted form in speech. Other languages may or may not choose to follow these orthographic conventions.