There is no or here. Gravity is the name of the force that accelerates you. It doesn't matter if you think you are pulled down or pushed up - a force is acting, and that force has a commonly accepted name: gravity
Do you know about the equivalence principle?
No. I took a brief look at wikipedia but what was described there seemed to either agree with what I am saying or have no relation to the discussion. If you have the time, could you try to briefly explain what you mean?
We have that exactly because there is a difference between gravity pulling you down and being in an accelerated frame of reference with regards to the forces in play. The fact that we in certain circumstances cant distinguish between them, does not mean that they are the same.
See that's weird, because wikipedia says:
gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.
Which seems to be in line with what I am saying. But perhaps I simply don't correctly understand what the principle means.
When you floor the gaspedal in your car, is it gravity pulling you back in your seat?
No. I wasn't saying that every force can be called gravity. I was saying that the force called gravity can be easily observed by anyone, at any time. How you believe gravity is caused has no bearing on whether or not gravity, as a force, exists.
Giving something a name, like gravity, does not make it a real thing.
It does - if a term has a definition, it is real. For it to exist in the empirical world, you of course need an observation - but gravity is constantly observed by anyone.