Center vs. centre
There is no difference in meaning between center and centre. Center is the preferred spelling in American English, and centre is preferred in varieties of English from outside the U.S.
Some people do make distinctions between the words. For instance, some prefer to treat center as the word for a place or institution and centre as the word for the middle point of something. But while these preferences may be taught in some schools and are perhaps common among careful English speakers in Canada, the U.K., and elsewhere, they are not broadly borne out in 21st-century usage.