I understand now, but I think any full frame that comes out of the GPU frame buffer is a frame. A real rendered frame or a generated frame using some algorithm. Even in the silly "I duplicate each frame" example, you are outputting that number of FPS. If you stand still in a game and nothing changes in the frame you're still counting all those practically identical frames.

A measure for "FPS effectiveness" sounds interesting. Like how much detail, changes, information can you discretely convey per second relative to what the game is continuously generating.

A Nyquist of sorts. Are you just duplicating samples? Are you sampling a high frequency signal (fast motion in the game) at high enough rate (lots of discrete FPS)?