British and American English not only differ in pronunciation, but they also sometimes use different words for the same thing. And for some same words they use different spelling. British English is still more influenced by the original French words like metre, litre, theatre, centre, manoeuvre you can still use in the English language, whereas the American words are more spelled like they are spoken.

Examples:

British: programme   →    American: program

Nowadays the American spelling becomes more and more also standard in international English. So if in doubt, you can always use the American spelling, which is usually a little moe simplified, respectively close to how it is spoken.

Attention: though you may find the word “thru” as a modern way to write the word “through”, we would still recommend to you to only use the spelling “through”. “Thru” is more used in informal and shortened text with people you know on an (almost) private level.

aubergine	eggplant	behaviour	behavior	analyse	analyze
ageing	aging	colour	color	apologise	apologize
aluminium	aluminum	flavour	flavor	emphasise	emphasize
boiler suit	coveralls	favourite	favorite	optimise	optimize
bogeyman	boogeyman	neighbour	neighbor	organise	organize
catalogue	catalog	pyjamas	pajamas	recognise	recognize
chemist	drug store	trainers	sneakers	zip	zipper
draught	draft	centre	center	travelled	traveled
dreamt	dreamed	fibre	fiber	traveller	traveler
grey	gray	metre	meter	travelling	traveling
jumper	sweater	kilometre	kilometer	modelling	modeling
jewellery	jewelry	theatre	theater	counselling	counseling
learnt	learned	manoeuvre	maneuver	counsellor	counselor
moustache	mustache	sombre	somber	fuelled	fueled
programme	program	spectre	specter	signalling	signaling
tyre	tire