A sample refers to a value or set of values at a point in time and/or space. The defining point of a sample is that it is a chosen value out of a continuous signal. The sample need not be discrete or digital (a common misunderstanding).
A theoretical sampler multiplies a continuous signal with a Dirac comb. This multiplication "picks out" values but the result is still a continuous function; just zero at non-sampling locations. If this signal is then discretized (i.e., converted into a sequence) and quantized along all dimensions it becomes a discrete signal.