Other than how they are spelled and where they are used, there is no difference between offence and offense. Offense is the preferred spelling in the United States, and offence prevails in all the main varieties of English from outside the U.S.
The American spelling gained steam through the 19th century, after being promoted in Noah Webster’s 1831 dictionary and all later editions, but didn’t become the more common form in the U.S. until the early 20th century. The spelling was not invented in the U.S., however. Webster and his contemporaries, in forging what they viewed as a more logical and more American variety of the language, actually just revived an old spelling that had been appearing to varying degrees since the 14th century, long before the United States existed. The Oxford English Dictionary cites examples of offense from as long ago as 1395—and their earliest instances of offence are from just a decade earlier—though it is true that the modern British spelling was settled by the 17th century and that offense was no more than a rare variant by the time the Americans adopted it.
Regardless of spelling, the word is usually pronounced OFF-fence in sports-related contexts, and off-FENCE in all other contexts. There’s no good reason for this difference. Blame sports commentators.
The veteran tight end never found a home in Mike Martz’s offense and was inactive for all but five games. [Chicago Sun-Times]
No offense to the many women who do far more gaming than I do, but I suspect that males were a not insignificant part of G4′s market. [Time]
If people take offense at hackneyed phrases it’s because they’re hackneyed. [The Atlantic]