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Comoving and proper distances are two cosmological distance conventions. For simultaneous radial separations in an FLRW model, proper distance equals the comoving radial distance multiplied by the scale factor at that cosmic time. A comoving coordinate remains fixed on an ideal comoving observer's worldline.

A comoving coordinate remains fixed for an observer following the homogeneous cosmological expansion.

A comoving coordinate provides labels for the comoving and proper distances comparison; proper separation additionally contains the cosmological scale factor.

Comoving radial distance uses the coordinate $\chi =\int dr/\sqrt{1-k{r}^2}$ and removes the radial curvature factor.

This radial coordinate is the comoving member of the comoving and proper distances comparison; multiplying by the scale factor gives proper radial distance at fixed cosmic time.