Proper motion in this context is simply motion relative to the frame of reference (the usual local idea behind Doppler shift).
Originally Posted by TOEfetish
When we talk about nearby stars, the term proper motion usually refers to only the motion in the plane perpendicular to our line of sight, and so it is measured in milliarcseconds/century or similar units, while the motion along our line of sight in that context is called radial velocity.
Outside that particular context, we mean simply motion relative to the observer... though when looking cosmological distances, we distinguish between "motion from the expansion of space" and "proper motion", where two particular galaxies in the same cluster (for example) may have very different motions relative to us, one orbiting the center toward us, and the other going away...
Forming opinions as we speak