OE (or O.E.) is Original Equipment. In short, these are factory original parts and are supplied to the auto manufacture for their use in new cars. These items must also be made by the same company that makes the factory original part.
OEM (or O.E.M.) is Original Equipment Manufacturer. This designation identifies a company as a supplier to a particular auto manufacturer. Products made by OEM companies may or may not be exactly the same design as the original part but are assumed to be the same quality, engineering standards, and manufacturing procedures to which auto manufacturers require.