Both "center" and "centre" refer to the same thing. As nouns, they signify the "middle" part or point of an area. As verbs, they refer to the action of placing something into the middle of something else.
So why are they spelled differently, what is the difference between them and in which situation you should use each, in order to be considered linguistically elegant? Let's see what English grammar experts have to say about this!
Center vs. Centre
There is no difference between these two words; both forms are officially accepted, according to several notorious publications and dictionaries, including "Cambridge Learner's Dictionary". The only essential aspect that makes a difference between these two forms is represented by the region where they are generally used. "Centre" is preferred in UK while "center" is the commonly used US version.
When do we use "center"?
When we are in the US. American English speakers definitely prefer to spell the word like this for an easier pronunciation. If you are writing an official message towards an American person/company, then definitely choose "center".
When do we use "centre"?
Surely if you are not going to prefer this version, nobody will feel offended by your choice. Yet, for more elegance in a formal message towards a British person, "centre" is much preferred in UK.
While you will not be criticized no matter which version, "center" or "centre", you use, your efforts to use the more appropriate version according to the person you are writing to will certainly be appreciated, especially in the UK, where people tend to be more careful to these aspects and more appreciative towards those who make the more "traditional" choice. Just remember to use "centre" in British English and "center" when you communicate with an American, and your grammar will definitely be impeccable in this matter.