How Many Kinds of Mass Does the Higgs Boson Mediate?

[dylankarr.com]

Ok, newb question. I understand that the Higgs mediates 'mass'. But the graviton (if it exists) mediates gravitation, right? So I assume this means mass is being treated separately, with the Higgs mediating inertial mass and the graviton mediating active gravitational mass, right? So what about passive gravitational mass, and relativistic mass/energy? Are they mediated by these same bosons? If so, which? Is energy/effective mass, as I'm thinking, something different that isn't really mediated? If so, why does gravitation increase with an increase in energy, rather than just rest mass.

Basically, if mass, rest, active gravitational, passive gravitational, inertial, etc. isn't all the same thing, where's the distinction? How many kinds of mass are there? What are they? And which boson are they mediated by? Higgs, graviton or something else?

 

[Blogical]

Higgs boson are the mediators in the theory involving a scalar bosonic field giving rise to inflation just after the Planck time!
Higgs mediate this scalar field and hence as this field is a gauge field, Higgs belong to the class of gauge bosons.
Its the only fundamental scalar boson in the standard model.
Higgs boson neverthless is the mediator of the higgs field which solves the problem regarding the breaking of electro-weak gauge symmmetry.
I could not understand the remaining part of your question.