To me, there's no difference between OE and OEM. The "M" in OEM stands for Manufacturer (as HandyHowie states in comments). OE/OEM is used to denote that the part was produced by the company who built whatever vehicle originally. For instance, if you have a Toyota, the replacement part would be made by Toyota.
Three things of note:
- A lot of aftermarket parts manufacturers use the same or slightly modified part number which matches what the OEM number is ... it makes it easier to align what you're buying to what you're replacing.
- A part which is manufactured by the aftermarket are usually made to the same specification as an OEM part ... ie: meets or exceeds OEM specifications.
- If aftermarket part has the OEM part number on it, it won't have the OEM logo on it. NOTE: This isn't hard and fast. In your case, you may not see the logo printed on the backside of the timing belt if it has worn off. You will (most likely) see it on a new timing belt which is OEM, though.
It is my experience not to frown on aftermarket parts. There are many good brands of aftermarket parts which are good parts and will last the change interval without issue. On the other hand, the only way you can go bad with using OEM parts is through your pocketbook, because they are usually more expensive than the aftermarket.
At some point, OEM gives up on making and stocking parts for vehicles. When this happens, you have to go to the aftermarket in order to keep your vehicle running correctly.