The difference between Behind-the-Ear (BTE) and RIE hearing aids is that on RIC/RIE the receiver sits directly in your ear, while BTE hearing aids have the receiver built into the body of the hearing aid.
Receiver-in-Ear (RIE) hearing aids
RIE hearing aids are one of the most popular types of hearing aids thanks to their ease of wearing and effectiveness. RIE hearing aids are also sometimes called Receiver-in-Canal hearing aids (RIC).