The Star next to someone?

WHat does the star next to the person in Quest mode mean? Does it mean I defeated that person? Also, there are people without stars next to tehir name when i go and see who I beat in Quest. WHat are the differences? Thank you

 

The star means you have defeated that opponent in the past. If you see a name in the arcade list with no star - it means you met them and have not beat them.

 

Thanka a lot. I didn't see this explanation in the instruction booklet.