Yes — that’s essentially how it works. A lens projects an image circle onto the film or sensor plane, and the camera records only the part covered by the sensor or film, which is usually rectangular.

So even though the lens is round, the recorded photo is rectangular because the recording surface is rectangular. The parts of the image circle that fall outside the sensor/film area are not captured.

There are a few exceptions or variations:

• Circular fisheye lenses intentionally project a smaller circular image that fits inside the frame, so you see a circle with dark corners around it.
• APS-C or other “digital-optimized” lenses may project a smaller image circle sized for smaller sensors.
• Tilt-shift lenses often project a larger image circle so the image can be shifted without losing coverage.

So your diagram is basically correct: the lens forms a circular image, and the sensor records a rectangular portion of it.