Basically, your idea that "...the combined action of both (i.e. that the Universe is expanding and an actual speed of removal of the galaxy)." is correct. The one due to expansion might be called "comoving velocity" while the one due to the "actual" motion of the galaxy through the expanding universe is usually called the "peculiar velocity".
The observed difference in velocity between two galaxies has two components, one is the comoving velocity (due to the expansion of space) and the other is the "peculiar velocity", which is the velocity due to motion distinct from the expansion. This is pretty easy to define mathematically. If we take a coordinate system that expands at the same rate as the universe, and call the radial coordinate $\chi$ ("comoving coordinates"), then the radial coordinate in the expanding universe $r$ ("proper coordinates") is related to the comoving coordinate by the scale factor $a(t)$, which describes the size of the relative size of the universe as a function of time (so if $a(t_1)=0.5$ and $a(t_2)=1.0$ the universe is twice as large at $t_2$ than it was at $t_1$).
$$r(t)=a(t)\chi(t)$$
The "proper velocity" (e.g. the example measurements you give in your question) is, intuitively, $\dot{r}=\frac{dr}{dt}$. This breaks down into two components:
$$\dot{r} = a\dot{\chi}+\dot{a}\chi = v_\mathrm{peculiar} + v_\mathrm{comoving}$$
A galaxy will have some peculiar velocity due to its $\dot{\chi}$, and all galaxies have (sort of) random peculiar velocities which lie in some typical range. So as you look further away (bigger $\chi$), the comoving velocity begins to dominate over the comoving velocity ($\dot{\chi}$ is the same everywhere, within some scatter).
You can measure velocities relative to any reference point you choose, it is completely equivalent to say one galaxy is moving away from another at $2000\;\mathrm{km}/\mathrm{s}$ or that they are both moving away from some central point at $1000\;\mathrm{km}/\mathrm{s}$ in opposite directions. In practice we usually measure everything from our vantage point, at rest with respect to the Milky Way (the motion of the Earth around the Sun and the Sun around the galaxy are known and usually corrected for).
