A refinish is simply a cuemaker taking your cue and restoring it, as best as he can, back to the original state, although it will often be better than original due to the newer clear coats, etc. Cost for a refinish is usually $150-300, depending on the cue, its original condition and who does the refinish.
A cue conversion is the act of taking a very old cue, such as the old Brunswicks and Willie Hoppe cues, and "converting" (making an entirely new, different cue) out of what you began with. The old cues were usually very thick, which is not very popular today, but the veneers, etc look great. A top cuemaker can begin with one of those old 1 piece cues, or an old butt, turn it down to new cue specs, make a new joint on it, new butt, inlays, wrap, etc, AND THEN make 1 or 2 new shafts for it, and you have an entirely new, beautiful cue. Cost will certainly run several hundred dollars, and can easily top $1000 for someone like Scruggs, Hercek, Searing, Tascarella, or the like to do the work,