Both forms are correct. Centre and center are both correct forms of the same word, so they have the same meaning. The main difference between these forms is that centre is a British English form and center is American English. These words are a common example of the differences in endings between British and American English, where British English words end with -re and their American equivalent with -er. When it comes to pronunciation, the difference is not noticeable, both are pronounced as / ˈsɛn tər /.

Correct spelling, explanation: form used in American English.

Correct spelling, explanation: form used in British English.

Definition of centre/center:
noun: the middle point of something;
Meet me in the town centre after school.
– someone or something that everyone is paying a lot of attention to or what is most involving;
Jenny always loved to be the centre of attention and now she works on TV.
The playground issue was at the center of discussion at the last community meeting.
– a place or a building where a specific activity happens;
After work, I have an appointment at the health centre, and then I have to pick up Jack from his football practice at the sports centre.
verb: to place something in the middle; to put at or around some central area;
A little to the left, this picture needs to be centered perfectly.
– to focus an action;
This novel is centered on the problems of human existence.