Strictly, what you mean is *specific* humidity; amount of water vapor per unit
mass of air. Absolute humidity is *total* amount of water vapor in air, which
depends on sample size. Also, relative humidity is (existing) water vapor
pressure divided by saturation water vapor pressure. Thus, it is as you
explained, but for vapor pressure rather than "amount". They are almost same.

Actually, "absolute humidity" is usually taken to mean "mass of vapor per unit volume." A.k.a. water vapor density, or rho_v.

rho_v = rho_air * specific humidity