It was George Bernard Shaw who said that Britain and America were “divided by a common language”, and this is brought home quite forcibly when we look at our rules of spelling!
In the UK, the English language has evolved over many centuries, and the way we spell our words today has not always been how our ancestors would have done so. Emigrants to the New World took the English language with them in the state that it was at the time, and there has been a certain degree of divergence since then, although there are many examples that show that it is the British spelling that has changed in the meantime, not the American.
There have also been several deliberate attempts at spelling reform in the United States, most notably by Noah Webster of dictionary fame, and Melville Dewey, who devised the Dewey Decimal Classification for libraries and preferred “catalog” to “catalogue”. Spelling reforms have also been proposed in the UK, but with much less success. However, the constant cross-fertilisation supplied by American books, journals and (especially) web-based materials has led many British people to accept American spellings in daily use.
So what are the differences? One that is now becoming very blurred is “-ise” and “-ize” as a word ending. This writer would always prefer to see “recognise” rather than “recognize”, regarding “-ize” as an Americanism, but some British dictionaries now give “recognize” as the preferred form. However, this “rule” – if it is a rule – only applies to words of two or more syllables; for example, don’t confuse “prise” and “prize”, which are words with entirely different meanings.
One very clear difference is the American omission of the “u” in “-our” word endings. So whereas a Brit would write “neighbour”, “harbour” and “colour”, an American would write “neighbor”, “harbor” and “color”. The important thing to remember here is not to use both forms of spelling in the same document; decide which spelling code to adopt and stick with it.
There are some examples where spelling reform has led to confusions that do not occur in British English. For instance, a floor of a building is a “storey” in Britain but a “story” in the USA. However, a “story” is also a tale that is told, on both sides of the Pond. In the plural, both “storeys” and “stories” are correct in the UK, depending on the context.
Another example is “kerb” and “curb”. If you hold something back, you curb it. If that something is the edge of a pavement (or “sidewalk” to an American), a Brit will do so with a “kerb”, but in American English “curb” is used for both meanings, and the special meaning of “kerb” has been lost.
To go beyond spelling, there are many differences that concern word choice and which are not a matter of words being spelled differently. The pavement/sidewalk example mentioned above is one of a huge number of potential sources of confusion. Ask for chips in the States and you do not get fried chipped potatoes but what Brits would call crisps! Make a mistake when writing in pencil and you would reach for a rubber in Great Britain, but ask for one in the US and you would get something very different!
American punctuate differently from Brits. The rule in British English is that the full stop (or “period”!) is always the final mark in a sentence, but Americans will happily place closing quotation marks or brackets after one. Americans insist on the opening word after a colon (:) having an upper case initial, which is anathema to grammatical Brits. Write a list of things ending “and …” and an American will place a comma after the last word before the “and”, but a Brit will not. There are plenty of other differences as well.
This is not to say that one way of spelling or punctuation is correct and the other is wrong, only that these differences exist and it is important to be aware of them, so that when writing in English you are consistent. However, as mentioned above, things are not always completely cut and dried and you can be forgiven for not getting it right every time – very few native-born writers of British English do so anyway!