In terms of a sensor or a detector, I would venture that the intrinsic error is the intrinsic noise in the detector - For a light detector this might be thermal noise, shot noise, dark counts etc, and to be differentiated from noise in the signal you are trying to detect.
In other words, the intrinsic noise is the noise you add after detection has taken place. The total noise is then the noise in the signal you are trying to measure plus the intrinsic noise of the detector.
Claude.