In signal processing, sampling is the reduction of a continuous-domain signal to a discrete-domain signal.
A common example is the conversion of a sound wave (x(t), a continuous-time signal) to a sequence of samples (x[n], a discrete-time signal).
A sample refers to a value or set of values at a point in time and/or space.
A sampler is a subsystem or operation that extracts samples, x[n]=x(nT), from a continuous-domain signal. A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous-domain signal at specified sampling instances.