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The Beat Riders are the term that refers to the dance groups that a most of the Riders using Sengoku Drivers came from.

Armored Riders are the Riders that use Sengoku Drivers and mostly come from these Dance teams (Bravo and Zangetsu being exceptions).

New generation (Or Energy) Riders are the Yggdrasil guys that use Genesis Drivers and energy lockseeds to transform.

The Armored and Energy Riders are still considered Kamen Riders. "Kamen Riders" as a term now has been mainly used in crossovers to unify all of the main Riders (I.E. "We're the Kamen Riders" rather then them being on their own and just being called Faiz, or Wizard, e.t.c.)