Do you speak British or American English? Depending on your answer, you may differ on which spellings you favor.
Center and centre have the same meaning. Center is the correct spelling in American English, but British English writers usually prefer centre. Notice that center (and centre) can be a noun, adjective, or a verb. Seeing the two words in real-life examples may help you to visualize how to use them.
Center in American Publications
Here are some quotes from the Internet.
Centre in British Publications
Center and centre are both correct spellings of the same world. However, where you live influences which spelling is most acceptable. If you like to learn about the differences between American and British English, you will enjoy researching the spelling of realize and dreamed.