I can potentially see (via thought experiment) a difference between gravity and inertial mass...
Picture two identical hypothetical objects, each a mile long with identical large masses at the end of a thin support rod.
Place one on the Earth with the mass resting on the thin support rod, one mile from the surface.
Place the other similarly on the nose of a 'space ship' accelerating at exactly one gravity.
The mass leading the spaceship by a mile will experience exactly one gravity while the one spaced a mile above the Earth (a one gravity reference) will experience LESS than one gravity due to it's distance from the gravity source.
Don't like the small difference? Make the rods 10 miles or 100 miles long. At each increase the gravity effects on the Earth reference device will be reduced more due to distance from the source, while the apparent gravity experienced by the space ship based device will still be the exact same 1G.
Now step back from this and realize that it means that the effect of gravity, such as from the Earth's mass, is different for each part of ANY other mass, depending on its distance from the source, while the effect is IDENTICAL for each part of any mass experiencing "pseudo" gravity due to constant acceleration, no matter where located.
It would make more sense in pictures, and even more in mathematical terms, but I am not even going to try. I quit doing that sort of stuff 30 or 40 years ago.
Maybe someone can bother to rough it out and see what shows up?