I think in England an apartment has to be completely self contained - it's own seperate services (gas, water, heat, electric - each billed separately to individual apartments)
But a flat has to be a flat and not an apartment if it shares some services. Like if you converted a house into two "flats" that use the same boiler or something, they cannot be "apartments"
However I think it's different in america because NY style "apartments" often have communal services.
I don't know where I plucked all that from, I'm pretty sure I read that from a reliable source somewhere at some point LOL :-D