A rotary evaporator is a device used for the efficient removal of solvents from samples by evaporation under reduced pressure. Rotary evaporation is most often and conveniently applied to separate low boiling solvents such a C6 hydrocarbon from compounds which are solid at room temperature and pressure. However, careful application also allows removal of a solvent from a sample containing a liquid compound if there is minimal co-evaporation (azeotropic behavior), and a sufficient difference in boiling points at the chosen temperature and reduced pressure.
Rotary evaporator is most commonly used when you want to remove a solvent. The liquid deposits a film on almost the entire surface of the flask. This film allows for a large surface area and the liquid evaporates faster. This method of removing a solvent is most commonly used when you want to remove a lot of solvent.
Short path distillation is often used for compounds which are unstable at high temperatures or to purify small amounts of compound. The advantage is that the heating temperature can be considerably lower at reduced pressure than the boiling point of the liquid at standard pressure, and the distillate only has to travel a short distance before condensing. A short path ensures that little compound is lost on the sides of the apparatus.
A short path distillation is pretty much the most crude type of distillation, the reason you wouldn’t want to use this is because it doesn’t have very good separating power and is a bit slower than a rotational evaporator. That said, short path distillation is cheaper and doesn’t need a vacuum pump.