There is one more to 'ise' and 'ize'. It is 'yse'!
Straight from the OxfordDictionaries:
Many verbs that end in -ize can also end in -ise: both endings are correct in British English, though you should stick to one or the other within a piece of writing. For example: finalize/finalise; organize/organise; realize/realise.
But there is a small set of verbs that must always be spelled with -ise at the end and never with -ize. The main reason for this is that, in these words, -ise is part of a longer word element rather than being a separate ending in its own right. For example: -cise (meaning ‘cutting’) in the word excise; -prise (meaning ‘taking’) as in surprise; or –mise (meaning ‘sending’) as in promise. Here are the most common ones:
There are also a few verbs which always end in -yse in British English.
and so on...
In American English, they are all spelled with the ending -yze
You can read more about the use of ‘ize’ and ‘ise’ on the Oxford Dictionaries blog. Here you will find more information about the historical usage of ‘ize’ and ‘ise’ and the difference between the two in the context of British English and American English.