Exactly! But a British cupcake is something slightly different; here is an image of a typical one:
http://www.englishcakelady.com/wp-content/uploads/2011/07/EC...These are of course only one subset of all 'cupcakes', but the kind possibly most familiar to British cake-lovers; this looks like an industrial one, similar to the vile but immensely popular 'Mr Kipling' range.
The key feature of the cupcake is the flat top and thick fondant icing; it is 'cup' because of course they are baked in individual paper 'cups' ('baking cases').
My Mum always used to differentiate 'fairy cakes' (usually with fancier toppings) and flat-topped 'cupcakes'; it could be that was just family usage.
Anecdote: when she'd burnt the tops of the fairy cakes, she'd cut them off and they'd suddenly become cupcakes ;-)