Organization, authorization etc. are the original English spellings pre 1776. This is why the 'Z' is still used all over the USA since any changes to the English Language after that date (American Revolution) by British authorities would have no jurisdiction in the USA.
However to find out which is correct in British English today, all you need to do is look in the Oxford English Dictio
I would have viewed the difference in terms of their usage in English Language, Organisation would be a verb, while Organization a noun. Example: The Organization I work with would pay for all my expenses. (Noun) The downfall of the project is in its organisation. (Verb)