No one and nobody mean the same. Nobody is a little less formal than no one. We use no one more than nobody in writing:
I knew nobody at the party.
No one moved; no one said anything.
We write no one as two separate words or with a hyphen: no one or no-one but not noone.
Nobody, no one, nothing, nowhere are stronger and more definite than not … anybody/anyone/anything/anywhere:
I did nothing. (stronger than I didn’t do anything.)
She told no one, not even her mother. (stronger than She didn’t tell anyone …)
We don’t use not + anyone/anything/anywhere as the subject of a clause:
Nothing will make me change my mind.
Not: Not anything will make me change my mind.
We don’t use nobody, no one, nothing, nowhere after no, not, never or other words which have a negative meaning (hardly, seldom). We use anyone, anybody, anything, anywhere:
I can’t do anything.
Not: I can’t do nothing.
She talks to hardly anyone.
Not: She talks to hardly no one.
