Science pretends there are two different sorts of mass, because our scientists cling to "magic forces" (actually they say there's three `masses'  when including `energymass').
Which means they have to define weight or how `gravitational mass' changes with your local `gravity', as a product of an imaginary `gravitational force'.
While claiming that inertial mass, unchanging wherever you go in the Universe, is a product of an equally imaginary `electromagnetic force'.
We say that `gravitational attraction' is only a shadow in the field conveying inertia and giving matter its inertial mass  the only real mass.
This is dangerous territory. Nonuse of formal terminology leaves us at the mercy of pedants, bores & `science' hairsplitters
Here's what the text books seem to say
Gravitational mass
Gravitational mass is said to be that which interacts with a `gravitational field' to give a body its apparent weight.
A body is given that weight by the product of its density / volume and the gravitational field.
[Gravitational mass depresses the scales]
So the text books said gravitational mass was a result of the `Gravitational Interaction'
Inertial mass
Inertial mass is the product of a body's volume/density which will give the resulting moment of inertia and therefore kinetic energy of a body moving relative to another.
[Inertial mass packs the punch]
So the text books said inertial mass resulted from the `Electromagnetic Interaction'
'Frame of reference'
Gravitational 
The gravitational attraction between masses is said to be determined by M_{1} × M_{2} × 1/d^{2};
[ignoring `Relativity' and `Quantum' arguments]
in other words: directly proportional to (increasing with) both masses but indirectly proportional to
(decreasing with) the distance between them.
Therefore Newton (and Einstein) said that the main gravitational influence on a body is going to be the largest and nearest mass or masses.
This is said to be the gravitational frame of reference and as you can see, the `gravitational field'  being a `local' shadow in a first order effect  seems to be a 'local' frame.
But gravitational `attraction# acts instantaneously and therefore really is in a universal frame.
Inertial 
Demonstrates `Mach's principle'  remember that pendulum at the North Pole? You read about it at "Blind Science"
It swings from/to opposite points, from say, Cassiopeia to Ursa Major and back, ignoring Earth's rotation, apparently `ruled by the fixed stars'.
Therefore Mach said that the inertial influence on a body is that of all the surrounding masses in the universe, regardless of distance.
This is called the 'inertial frame of reference' and as you can see it's an entirely 'nonlocal' (universal) frame.
Reality
'Inertia', 'inertial mass' and the 'inertial frame of reference' (and ditto for 'gravity')  are at the heart of physics
But conventional science hasn't the least idea of why they work or indeed of what they really are  as you can see from the text book quotations above (and by modern scientists' disputes).
'Inertia' is an attribute of any body of matter; being what you must first overcome to start moving, and overcome again to stop. It is unaffected by 'gravitational fields' and remains the same for a given mass whether on Earth or in Space
'Gravity' is a socalled 'force' pushing* material masses together [*despite scientists' claims  a pull doesn't exist in this Universe]
What causes all the confusion & disputes of mainstream scientific theorists?
The reality  that:
'Inertia' is a direct (primary) effect of UEF's interaction with mass
The inertial frame is universal. We say it is 'instantaneous' throughout the universe
`Gravitational attraction' is merely a 'shadow' cast by matter in the UEF  details at abolish. Because the 'shadow' is a radiated effect it is ruled by the inverse square rule.
Working details?
footnotes3 & abolish
Notes:
`Weight' is how much your `inertial mass' gets pushed towards another body. It's a vector quantity.
The various "masses" defined (and discussed)
Also see Reader's Mail 1 & Reader's Mail 2
Reaction of mass held in rotation, or released: "Centripetal or Centrifugal Force" Reaction of mass to varying radius of rotation: "Conservation of Angular Momentum" Reaction of mass to varying angles of rotation: "Precession" Reactions of mass to other movements: "Coriolis Force" 
