Yes, that the account has paid Elon for a blue check. Originally it meant that the user was in fact who they appeared to be. Then it became a status symbol, then Twitter removed it on a couple of occasions for saying something they disagreed with, then came the accusations of Twitter admins being capricious about the whole process and essentially taking personal bribes in exchange for checks, then Elon bought it and made it a paid feature.

The grey check indicates the identity of an government or non-profit has been verified and the account is who it says it is.