What is the difference between the words centre and center?
This is one of the reasons why Oscar Wilde described America and Britain as "two great nations divided by the same language."
The words are identical in meaning, but "center" is an American spelling. I believe it's a result of Noah Webster's efforts to rationalize American English spelling in the early 19th century: he also dropped the "u" in "harbour" and "colour" and tried to establish "thru" for "through," and "nite" for "night."
British English borrowed a lot of words from French, including the spellings. Usages like "centre" and "theatre" persist not only in the United Kingdom but also in Canada and other parts of the former Empire. It's become a way of distinguishing one's identity.
In fact, Canadian newspapers and magazines used to use American spellings if they made the word shorter (like "harbor" and "labor"), but they went back to mostly British spellings in the 1980s because their readers preferred it. (We always spell words like "curb" and "tire" the American way—not "kerb" and "tyre.")
However, my Funk & Wagnalls Canadian College Dictionary gives "center" as the preferred spelling, with "centre" as "Brit." for "center." When spelling it in the British style, we are to also to write "centred" and "centring." So Canadians would have to be self-consciously British to spell it "centre."
While English spelling is chaotic and inconsistent, we would be worse off with phonetic spelling. English dialects have so many differences in accent and pronunciation that we would have big trouble understanding people writing phonetically in their own dialect. "Emma Chizzit" is supposedly Australian for "How much is it?" And I'll always remember the time a New Zealand friend baffled me with a comment about "Eric's lend load." Turned out he meant "our ex-landlord."