For some reason, English has two parallel sets of indefinite pronouns for people: no one (no-one or noone) and nobody, someone and somebody, anyone and anybody, and everyone and everybody. There is no particular reason to choose one or the other, apart from consistency, if that is important for you.
According to Dictionary.com, based on the Random House Dictionary, nobody and anybody developed before no-one and anyone, someone and somebody developed together, and everyone developed before everybody. According to Google Ngram Viewer, anybody, somebody and everybody were more common in the 19th century, but anyone, someone and everyone took over between 1900 and 1930 (slightly earlier in British English than in American English), and are now considerably more common. Conversely, no one has been more common than nobody since before 1800.
My own usage is very clear: in my Korean diary (2006-09, 225,000 words) I used no-one 66 times, noone 4 times and nobody once; anyone 45 times, someone 137 times and everyone 70 times, and anybody, somebody and everybody nonce. (Some of those occurrences were quotations of other people or written sources.)
Is there any difference in meaning? As indefinite pronouns, apparently not. Dictionary.com defines no one as ‘no person; not anyone; nobody’ and nobody as ‘no person; not anyone; no one’, someone as ‘some person; somebody’ and somebody as ‘some person’, anyone as ‘any person at all; anybody’ and anybody as ‘any person’, and everyone as ‘every person; everybody’ and everybody as ‘every person’. (Note that the ‘one’ form is defined as the ‘body’ form more often than vice versa.) It also notes that ‘Anyone is somewhat more formal than anybody’ and, predictably, ‘Anybody is less formal than anyone’.
Nobody has a secondary meaning of ‘a person of no importance, influence, or power’, somebody ‘a person of some note or importance’ and anybody ‘a person of some importance’ (their illustrative quotation: ‘If you’re anybody, you’ll receive an invitation’) (but compare ‘a nobody’, ‘a somebody’). Body also retains its ‘real’ meaning: ‘no body was decayed’, ‘some bodies were decayed’/’if some bodies are decayed’, *‘any body was decayed’/‘if any body is decayed’, ‘every body was decayed’. (This also shows that ‘some’ by itself has a plural meaning and verb agreement. [PS – it’s more complicated than that: compare ‘Somewhere in the world, some person is happy’ and ‘Somewhere in the world, some people are happy’.]) On the other hand, one also retains a meaning as a (rather formal) pronoun, meaning either ‘I’ or ‘anyone’.
There is also the issue of ‘two words’, ‘hyphenated’ or ‘one word’: ‘no one/no body’, ‘no-one/no-body’ and ‘noone, nobody’ etc. All were originally two words. While someone and somebody, anyone and anybody, and everyone and everybody, and nobody are the more common forms now (and have been for some time), no one is more common than no-one, and noone is very rare (and is red-underlined by the spell-checkers in Pages for Mac and here on WordPress). (My own usage is clearly ‘no-one’ – see above.)