Clipped forms can pass into common usage when they are widely useful, becoming part of standard language, which most speakers would agree has happened with math/maths, lab, exam, phone (from telephone), fridge (from refrigerator), and various others.
Examples: fridge (refrigerator), Polly (Apollinaris), rona (coronavirus), shrink (head-shrinker), tec (detective); also flu (which omits the stressed syllable of influenza), jams (retaining the binary noun -s of pajamas/pyjamas) or jammies (adding diminutive -ie).
Examples include ad and advert (advertisement), cable (cablegram), doc (doctor), exam (examination), fax (facsimile), gas (gasoline), gym (gymnastics, gymnasium), memo (memorandum), mutt (muttonhead), pub (public house), pop (popular music), and clit (clitoris).
Examples: bot (robot), chute (parachute), roach (cockroach), gator (alligator), phone (telephone), pike (turnpike), varsity (university), net (Internet).
They may be further subdivided into two groups: (a) words with a final-clipped stem retaining the functional morpheme: maths (mathematics), specs (spectacles); (b) contractions due to a gradual process of elision under the influence of rhythm and context.