Realise and realize are different spellings of the same word. Realize is the preferred spelling in American and Canadian English, and realise is preferred outside North America. This distinction extends to all derivatives of the verb, including realised/realized, realising/realizing, and realisation/realization.
Examples
For example, these British and Australian publications use realise:
Next time you realise you’re sucking in your gut, don’t feel ashamed. [Guardian]
I realise I will still have to lodge a tax return but what will happen if I get a job? [Herald Sun]
However, for the telco’s competitors, it’s a sobering realisation that the battlefields in the mobile sector have dramatically widened. [The Australian]
And what his devoted fans—known as Beliebers—don’t realise is that the battle between his warring parents is tearing the talented Baby singer apart. [Mirror]
And these American and Canadian publications prefer realize:
The industry is finally starting to realize this problem, but one of the first, flawed attempts to fix it only illustrates how much work remains. [Washington Post]
They don’t realize they have to stay active to qualify for free flights or luxury items. [Toronto Sun]
Linus apparently didn’t realize he was talking to Natalie Portman at one point, and his wife asked Warren Beatty who he was. [San Francisco Chronicle]
He has betrayed this realization in off-hand comments to Western intellectuals. [Wall Street Journal]
