It is the same thing but with different spellings. 'Center' is the spelling in American English; 'centre' is preferred in British, Indian, and Australian English. In Canadian English, 'centre' is the noun, and 'center' is the verb.
Another opinion relates to its usage in Commonwealth countries: 'Center' - the middle (as in ... I was in the center of the circle). 'Centre' - a physical location (as ... I spent the afternoon at the community centre)
Usage by American influenced countries is normally confined to using 'center' for both situations however there are exceptions such as the city of Sauk Centre, Minnesota.
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