Yes Optimization is spelt the American way not the English way of optimisation. The reason for this is simple. If you enter in the Google Search Engine ‘Optimisation’ (which is the correct English spelling.) Google will ask ..
Did you mean Search Engine Optimization?
The answer is yes and no. It is the Americanised spelling of the world. So this clearly indicates that you need to know your target audience. For example people in England looking to go on a vacation would not use the word vacation but the word holiday. So if you are an American company targeting British tourists you would get more searches for ‘New York Holiday’ than you would ‘New York Vacation’. It is all down to the regional relevancy of your target audience.