The "most valuable player to his team" is the "most valuable player," unless there is some other player eligible for the award who is not on a team. It's a tautology - the most valuable player is, by definition, the player who produces the most value, who is, by definition, the best player - the most outstanding player - in the league in that specific season.
I'm not sure where these other definitions of the Hart as "the biggest lead over his next teammate" or "best player on a marginal team" come from. Probably from sportswriters who view sports as some kind of morality play.
Those “biggest lead over his teammates., not sure who said that, likely Comes from the definition, most valuable to his team.
As in, is player 1 on team X, more valuable than player 1 on team Y is to his team.
And player 1 on team Z, is more important to his team than both X and Y are to their teams.
I know some writers have said, they literally go by that, as that’s the wording.
I’m sure the writers are using both definitions, that’s why I think a re-wording is necessary of trophy. I know some writers have said, they go
MOP - Most outstanding player in the league.