What is the difference between Time-Trial and Triathlon bikes? Time-Trial and Triathlon bikes differ from normal road bikes in that they are designed for maximum efficiency when riding alone (not in a group). 

What, then, is the difference between them? Would there be something wrong with using a TT bike in a triathlon, or vice-versa?

There doesn't seem to be an objective difference between the two, and I often see them lumped together as a category. Is there a significant (if any) difference between them?
They are very similar but have to follow different certification rules. For example, under UCI regulations the saddle of a TT bike must be at least 5 cm behind a vertical line drawn through the bottom bracket (cf. Rules 1.3.011 to 1.3.025), there are constraints on the size, shape, and orientation of frame members, and so on. Triathlon bikes are certified under a different set of rules depending on the race being run and allow a greater degree of integration of components (such as water bottles that are designed to fit within the frame in a way that enhances aerodynamics). Currently, any UCI-certified TT bike can be used in a triathlon but not all triathlon bikes are allowable in UCI-sanctioned races.