Do you distinguish this two points? I mean for me camera is a kind of small pyramid that floats in tha air, It has an eye point in rear but in general its centre point (the point around which it can rotate) is not neccesary the same as eye point. I call this two points eye point and camera point though i do not know official terminology for that. could you maybe say something more about this?
In terms of common terminology, these are the same.
You typically separate the camera from the camera controller. The point you rotate a camera around is determined and handled by the camera controller, not the camera. The camera has an eye position, view vector, and up vector (or some other data that is equivalent). The camera controller might have a position, distance, euler angles, zoom factor, rotational speeds, etc. (The presence of a zoom factor means that the camera controller also affects the projection matrix and FOV and not just the camera matrix).
Some engines conflate "camera" with other things like filters and render modes and post-processing settings. In such engines, you tell a "camera" to render and then it figures out what and how to do the rendering, but a separate camera controller still generally deals with moving the camera. In terms of the usual engine-agnostic terminology, the camera is just the base mathematical definition needed to construct a camera matrix, and everything else is part of the scene render pipeline or game logic.