Sophie, you might as well ask why dialect words in Aberdeen are different from those used for the same thing in Newcastle and why both of these are different from the words used in Bristol. All languages and the dialects thereof are constantly developing and evolving. Similarly, standard English in use today is very different from that spoken in Shakespeare's time.
It's hardly surprising, therefore, that American English vocabulary is frequently different from British English.
As regards ise/ize, the old rule - and one still largely followed by The Oxford English Dictionary (the English word-�bible') as well as American usage - was that words derived from classical Greek with the letter zeta in their suffix were rendered �ize' in English...ie retained the �z'. However, many modern publishers - including �The Times' newspaper - prefer the Latinate and more modern �ise' for most such words.
Thus, normal British usage has �organise', �apologise' and so on. Certain words - eg �capsize' - are never modified to have an �ise' ending. In the same way, there are others - such as �disguise', �analyse', �circumcise', �televise', �exercise' and �chastise' - which are never given an �ize' ending. Apart from the exceptions such as those mentioned above, you are basically free to use whichever form - ise/ize - you prefer!
I believe the ize form became the standard version in the USA when Webster produced his first dictionary there in the 19th century and opted for that variant.