When i say they're one of the closest, it doesn't necessarily mean they're close, just that a lot of the other, more closely related ones, such as mammoths, are extinct. That said, the closest living relatives to elephants are actually manatees and dugongs.

These are still different animals that evolved to fill different niches though. They're part of the clade Afrotheria, which is very, very diverse.

For more information on why this is such a diverse clade, i'd recommend Clint's Reptiles' video about it: https://youtu.be/bO2DpSJtFBo