While a bit political, this Vox article does a good job explaining the history of Captain Marvel.
Captain Mar-Vell (people generally called him Marvel) was a Kree. That's this guy:
Carol DanversCarol Danvers was originally someone who worked with Mar-Vell (Marvel Superheroes #13). She even had a romantic relationship with the Kree version. Later, she had a run-in with a Kree device that made her half-Kree. Once she realized she had powers like Mar-Vell, she took the name herself (the story there was Mar-Vell left Earth).
Generally speaking, when people refer to Captain Marvel, they mean Carol Danvers, since she's held the title longer (the original was canceled in the 70s).