Both are correct, and the meaning is the same. American English always uses the 'ze' spelling. Outside the USA, the standard spelling is 'se', although the 'ze' spelling is sometimes used and is becoming more common. If in doubt, it's probably easier to use the 'ze' spelling, as this is less likely to upset most spellcheckers. By the way, the same rule goes for all words ending in 'ise' or 'ize' - realise, recognise, materialise and so on.

Both are correct. Americans spell it with a "z" and Britons spell it with an" s."

both is true :) One is American use. another is English use.

Apologize is American and Canadian English, it is the original form, it is still used by some British publishers. Apologise is English outside North America,