Oh alright then. What's the difference between a contraction, an abbreviation, and what the COED calls a 'symbol'?
Well, a contraction is a phrase of two or occasionally more words, which occurs with enough frequency that it becomes one word, generally with the loss of some sounds at the boundaries between the source words. Sometimes an apostrophe marks the loss, as in 'can't', but sometimes there isn't one, as in 'gimme'.
That's right, innit?
At school I learned that we're only ever allowed one apostrophe per contraction, presumably because we're only allowed one site of elision - that is, one group of contiguous phonemes (sounds) which are lost in contraction. So 'wouldn't've' is forbidden in writing, even though it's common in speech.
I can see absolutely no reason for this rule. Except for the obvious one that English teachers like to make up silly rules which are obviously untrue.
An abbreviation...is just a few letters from a written long word or phrase, which we write because life's too short to write the full version. But sometimes we show it's an abbreviation by putting a period symbol (.) after it.
For some abbreviations, when we read them we substitute the full version - 'etc.' becomes 'et cetera', 'inc.' gets unfolded to 'incorporated'. And for some we just say the names of the letters - 'PLC.', 'DJ'.
Um. Unless the abbreviation can be pronounced as a word, in which case we sometimes do just that. 'GIGO,', 'Radar', 'Gosplan'.
And yes, if it's made up of the first letters of each word, it's an acronym.
So what's a symbol then? Well, it can be one of two things. Firstly, It can be a shape that isn't a letter of the alphabet, or sequence of letters, but represents a word - and when we read them, we tend to say them as words.
If we read the dollar sign ($), we tend to say 'dollar' or 'dollars'. The same sort of thing for the pound sterling sign (£) and the ampersand (&). They're shorthand. The obvious symbols which the COED forgets are the numerals - 1,2,3 etc - symbols which stand in for the words 'one', 'two', 'three' etc.
Plus (+), minus (-) and equals (=) all easily fit into this category, but what about the exclamation mark (!) and brackets ([ ])? They don't represent words - brackets are syntactic and the exclamation mark is what's called prosodic.
But for some reason, the SOED only lists the sterling symbol. The others it gives are alphabetic symbols - sequences of letters which represent words or phrases that are common enough to merit a short form, sometimes an abbreviation, but only in specialised fields.
'cm' is 'centimeter' (or 'centimetre' if you're (1) British and (2) old fashioned). 'kph' is 'kilometers per hour'. 'k' is 'kilobyte' but 'K' is 'kilobit'...unless you're a physicist, in which case it's 'Kelvin'.
'A4' is a size of paper if you're a secretary, and 'Au' is the element 'Lead' if you're a chemist...but 'AU' is 'Astronomical Unit' if you're an astrophysicist.
So. Here's the disappointingly small COED list of symbols.