...

I guess 's' is British and 'z' is American.

Chambers (of Cambridge, England) has both.

"z" used to be the British English standard. It is still preferred by the Oxford English Dictionary, and consequently, the Oxford Universtiy Press. The rationale is that "z" is the most sensible transcription of "zeta", and the suffix "-ize" derives from the Greek "iota-zeta-omicron-sigma". The Cambridge University Press currently prefers "-ise"; some time ago, the London Times switched to this point of view also. Most British publications now concur. "-ise" seems to be what Americans use; does this come from Webster's, like so much American orthography?