No, it is really a different bug. One is speculation around branches, the other one is speculation around hardware protection check (which is not implemented internally as a branch). In fact, while all OoO CPUs are vulnerable to spectre, not all of them are vulnerable to meltdown because, for whatever reason, their designers decided not to speculate around hardware checks (possibly because the check could be implemented efficiently in the critical path given their L1 cache design).
I'm not an hardware designer, but likely both instances of speculation use the same snapshot and rollback logic, but that's about it.
I'm not an hardware designer, but likely both instances of speculation use the same snapshot and rollback logic, but that's about it.