Clippings can be made by clipping off the beginning of a word, as in (tele)phone; by clipping the end off, as in ad(vert) and doc(tor) or by clipping bits off both ends, as in (in)flu(enza) and, with a bit of orthographic licence, (re)fridge(rator). Most clippings started life as informal uses of more formal words, but some have become so common themselves that many people may not actually know the full form of words such as bus (omnibus), mob (mobile vulgus) or cello (violoncello).
Nor, much to the chagrin of some language pundits, are they a modern fad: the 17th century essayist Thomas Addison, in a 1711 issue of The Spectator, complained about the way people "have miserably curtailed some of our Words" and goes on to cite incog. for incognito and pos. or pozz for positive.