Organise and organize are different spellings of the same word. Organize is the preferred spelling in the U.S. and Canada, and organise is more common outside North America. This extends to all the word’s derivatives, including organized/organised, organizing/organising, and organization/organisation.
When the word came to English from Latin via French in the 15th century, its primary spellings were organize and organyse. The spelling now preferred outside North America did not appear until a century or two later. Since then, organize has mostly maintained its ascendancy, though British writers in particular have been seemingly unable to make up their minds. This ngram graphs the use of the two spellings (as a percentage of all words) in a large number of British books, journals, and magazines published between 1800 and 2000:
What this graph shows is that at the turn of this century organize was the preferred spelling in some types of British publications. But as anyone with access to Google News can ascertain with a few minutes of searching, organise is now preferred, at least in news publications, which tend to reflect popular usage.
Having an efficient system to file and otherwise organize these documents can save frustration and time. [Los Angeles Times]
If organized labour is as great for workers as its supporters claim, why are so few people fighting to save it? [National Post]
Although they lost to New England, the Ravens’ organization remains stable. [Wall Street Journal]