There are many types of relays that you might not be aware of. I found on schrackrelays.com a good explanation 0f the main types of relays. There are three main types:
Neutral relay, non-polarized relay
A neutral, monostable relay operates independently of the direction of the energizing direct current.
A polarized, monostable relay only operates in a specific direction of energization. It then adopts the operating state.
A polarized bistable relay adopts one switching position on energizing in a particular direction and the other switching position when the energizing is in the opposite direction. In a bistable relay with one winding, the opposite energizing is created by a voltage with an opposite polarity being applied to the same winding. In a bistable relay with two windings, the opposing energizing is created by a voltage with a reversed angular direction being applied to the second winding.
Remanent relay (remanence relay)
A remanent, bistable relay adopts a particular switching position at an energizing direct current in any direction and is held in this position by the remanence in the magnetic circuit, i.e. through the magnetization of parts of the magnetic circuit. The contacts shift to the other switching position on a small energizing current of limited amplitude in the opposite direction. This demagnetizes the magnetic circuit again.
Relays types: Neutral relay, Polarized relay, Remanent relay - [Link]