For the SINAD he is right, I have deepened and on the tutorial Analog Device MT-003 we can see the following:
Total harmonic distortion plus noise (THD + N) is the ratio of the rms value of the fundamental signal to the mean value of the root-sum-square of its harmonics plus all noise components (excluding dc). The bandwidth over which the noise is measured must be specified. In the case of an FFT, the bandwidth is dc to fs/2. (If the bandwidth of the measurement is dc to fs/2 (the Nyquist bandwidth), THD + N is equal to SINAD—see below). Be warned, however, that in audio applications the measurement bandwidth may not necessarily be the Nyquist bandwidth.
On my 16-bit PicoScope 4262 laboratory oscilloscope there is both the THD + N measurement and the SINAD measurement and the S/N signal to noise ratio measurement, in particular the SINAD measurement seems to be more equivalent to the negated than the S/N.
For the sake of completeness I am attaching the Analog Device document.
As for the double display of the THD and THD + N values, I absolutely agree that they represent the same value in a different form, it was just for convenience because many times it is expressed as a percentage and others in db and having both could be useful when doing comparisons.
Thank you for your availability