When you talk about mag instead of magazine, fab when you mean fabulous, or cred for credibility, you are committing apocope, that is, leaving out the last sound, syllable, or part of a word. Perhaps it’s our rush-hurry-urgent age, but it seems that such energetic abbreviations are becoming more common, not merely with students who produce slangy in-terms such as psych, chem and maths (math in the US).
Apocope comes from the Greek word apokoptein, to cut off, made up of apo-, from or away, plus koptein, to cut. Spelling abbreviations like huntin’ or singin’ aren’t apocopic, because the missing last letter indicates that the final sound of the word has changed, not that it has been lost.
Incidentally, if you instead cut the sound off the start of a word, the right name is aphesis (an example being squire, an aphetic form of esquire); if you drop sounds in the middle (for which the classic — and extreme — example is fo’c’s’le for the crews’ quarters on board ship, in full forecastle), the process is called syncope.