The primary difference is shaft taper. Pool players tend to prefer the 'pro taper' where the portion that slides on or through your bridge is a cylinder of constant diameter, i.e., no taper in that last 10 or 12 inches. A carom cue generally has a conical or modified conical taper, where the last 10-12 inches simply continue the taper from the rest of the shaft. Snooker cues also tend to have conical tapers.
Carom cues (and snooker cues even moreso) also tend to have smaller tip sizes than pool cues generally have. There are also differences in length and weight.