Criticize and criticise both mean to point out faults or problems in something or someone, so the choice comes down to spelling style rather than meaning. Criticize is standard in American English and Oxford's British style; criticise is the spelling most other British writers use, as in "Don't criticise her work until you've heard the whole story."
The core difference
The words are identical in meaning; only the -ize versus -ise ending changes.
- criticize — point out faults or problems: The coach criticized the team's poor defense.
- criticise — the same word in everyday British spelling: Don't criticise her work until you've heard the whole story.
Which spelling should you use?
Criticize is built from critic plus the -ize suffix, the ending American English kept and Oxford dictionaries still favour in British text. Criticise takes the more common British route of -ise, the same pattern seen in apologise and recognise.
There is no meaning difference to trip over here, only house style: use criticize for American readers or Oxford-style British writing, and criticise for general British English.