Understanding "voltage" and "power" in SNR of a sampled signal
Handling units in signal processing is tricky (what are the units of $e^{s(t)}$?). I find it useful to think about operations on signals physically, instead of trying to make sense of them mathematically.

For instance, a mixer multiplies two signals. Let's assume the signals are measured in volts. The mixer output is, obviously, also a voltage. This is true even when one of the mixer inputs is its own delayed output.

When calculating an SNR, you square the signal sample (which is a voltage value). In this case, you get a result in watts, because it turns out that the signal power is equal to its square. Physically, you could connect a watt-meter to get a reading of the signal power; you would find that, at every instant, the power turns out to be equal (or proportional) to the square of each sample.

So why, when multiplying two voltages, you get a voltage in one case (mixer) and a power in another (SNR)? I think the reason is that you interpret the result differently in each case. In the case of SNR calculation, the square of a sample physically matches its instantaneous power, so you can assign that meaning to the mathematical operation.