A changing direction on the sky
Stars are not permanently fixed points in constellation diagrams. Measurements across epochs reveal changing directions, expressed as angles per year rather than direct displacements in kilometres.
Different proper motions gradually alter constellation shapes over long periods. Precise positions across time, rather than one naked-eye view, reveal the movement.
References: [1]
Separating proper motion and parallax
Observed positions combine stellar motion with the observer’s orbit. Annual parallax is periodic, while proper motion is commonly represented as a continuing trend over a limited observing interval.
Gaia estimates position, parallax and proper motion together from multi-year observations. Assigning every change between two images to the star itself would mix those effects.
Angular rate is not spatial speed
The same angular rate corresponds to different transverse speeds at different distances. Large proper motion therefore does not by itself identify the fastest star in space.
Proper motion supplies transverse information, while radial velocity describes motion along the line of sight. Distances and consistent reference frames are needed to combine them into three-dimensional motion.
References: [1]