All varying voltage values are "signals". A string of samples, derived from a continuous signal, is still a 'signal'. The fact that this signal is a string of samples, makes it special, though because it is the result of a Modulation process and we just describe it as 'samples'. All streams of digits in a circuit are also analogue 'signals' of course.
But 'sampling' is a different issue from Analogue to digital conversion, which also involves Quantising the information contained in the original signal.
In the 'Old Days', when we didn't have the luxury of digital processing, they used 'Sampling Oscilloscopes', which could produce an analogue display of a very high frequency signal (up in the GHz region) by sampling it at a low frequency with a stream of very short pulses. You needed to have a repeating HF signal and to sample at the appropriate rate but the 'scope gave you picture of the HF signal as a set of analogue samples. This was extreme sub-sampling and you had to be extremely careful in interpreting the display, of course but my point is that they were Analogue Samples.
If you want to convert an analogue signal to a digital one then the digital values need to be associated with particular time values on the signal. Hence, you 'sample' the continuous analogue signal and then convert that sample value. If you don't do that then your ADC process may get confused. There are all sorts of ADC methods but they all take time to deliver a value, in between sample times you could imagine all sorts of weird combinations coming out of 8 parallel bits. You need a 'clock' to sort all this timing out. Even if you don't actually use analogue pre-sampling, it is still important that the timing of the digital values is consistent with the timing of the values of the original analogue signal.
BTW, it is not necessary to sample at a regular rate as long as the reconstruction equipment (DAC) knows the timings of the individual samples (and as long as the sample spacing is narrow enough to satisfy the Nyquist criterion for that portion of the signal). A lot of bit reduction methods involve this strategy, aamof.