A Reflection Nebula is a cloud of Dust that is scattering Electromagnetic Radiation from one or more nearby stars, making it glow enough to be seen as a Light Nebula rather than a Dark Nebula (essentially a black spot).
A Cometary Nebula is one that resembles a Comet, and represents one of the ways some reflection nebula can appear from our point of view. In the classical case, it is a diffuse nebula lit by a star in such way that it resembles a comet with tail.
Cederblad Catalog (Ced)
Parsamian Nebula Catalog
Van Den Bergh Reflection Nebula Catalog (vdB)