I have read that the atmosphere in the ISS is pressurized to a standard sea-level atmosphere and also of the same composition (ratio of nitrogen and oxygen etc.). What I am struggling to find online is whether the air mass density in the ISS is higher than that on the ground. I think the air density up there is higher because here on the surface we have a large altitude of air in the atmosphere sitting and pressuring on us, where up there in the ISS it virtually is zero gravity, let alone having an atmosphere as thick as that on the surface. So my logic is that the pressure in the ISS has to fully rely on the momentum of free-moving air particles without gravity i.e. temperature and density of air in order to achieve an atmospheric pressure comparable to that on the surface, is that true?
I believe that you are incorrectly looking at the same pressure from two different points of view, and then adding the two points of view together!
Yes, at ground level on earth and in orbit in the ISS, the pressure exerted by the air on a surface is the result of adding all the random collisions of the air molecules with the surface. If the temperature, absolute pressure and gas compositions are the same, then the collision rates are the same, and the air mass densities in the two locations are identical.
We can ask, "Why do we have the particular conditions for the ground level gas? Why are that many hitting the surface each second"
It turns out that the air molecules are pushed close together by the weight of all the air molecules above the surface. In fact, the normal atmospheric pressure is a direct measure of the weight of the atmosphere above a unit area. But that doesn't mean that the two numbers should be added.
In the case of the ISS, the dense air mass is confined (hopefully!) by the walls of the ISS. These walls are in tension, and exert the same force on the air in the space station as the column of air exerts on the sea level air.