If a Star Moves in Space, Its Proper Motion Appears

If a star moves in space, its proper motion appears as an angular displacement against the background stars. Its parallax motion also appears as an angular displacement against the background stars. How can we tell the difference?

A) We cannot tell the difference. This is a major uncertainty in measuring either value.
B) We cannot tell the difference, so we measure proper motions only so far away that their parallax motions are vanishingly small.
C) We cannot tell the difference, so proper motions are estimated from radial values that are unaffected by parallax.
D) We can tell the difference because parallax motions are periodic while proper motions are not.