Yes, Rimuru is among the group of "awakened" demon lords, like Milim, Guy, Leon, Ruminas, and technically the little fairy, Ramiris, used to be one too. Draguel and Dino are unique cases. (Draguel moreso than Dino).
Clayman, Frey, and Carrion are basically just really strong humanoid monsters. (can't call them demons, cause that diablo and his type exist as the official demons of the story). Most, if not all, of the awakened demon lords were already aware of this. Rimuru picks it up quickly (partly due to super computer skill: Raphael).