The common technique of acquiring a digital representation of a waveform is to take consecutive snapshots of it in regular, equidistant instances in time. This is called Real Time Sampling or short RTS as the conversion in relation to the signals changing is done in real-time. A conceptual visualization of this type of conversion is shown in figure 1. The time needed to convert one sample into a digital value is denoted as Tc. The period of the signal which is the inverse of its frequency is denoted T. The instance in time at which a new conversion starts is marked with ts.
In the picture above S marks the duration for sample and hold which indicates that in this time period the input signal will actually captured that is a snapshot if its physical value is taken. After this time it will be converted to a digital value in the conversion phase marked with C. When the conversion had finished this loop may start again. In parallel the result could be used for further processing marked as R. This technique has a natural boundary in terms of how fast it can provide new samples which is the sum of the sample time and the conversion time. Thus limiting the highest frequency of the samples signal according to the sampling theorem of Nyquist-Shannon. To overcome this limitation a different technique of sampling named ETS [comp.  p.273ff] can be used although it introduces limitations on the applicability. The principle of ETS is shown in chapter Equivalent Time Sampling - Theory of this wiki.
The content of this chapter is taken from the master thesis "Development of a low-cost micro-controller based oscilloscope including equivalent time sampling" by Ing. Harald Schloffer, MSc, November 2016
Schloffer Harald: Development of a low-cost micro-controller based oscilloscope including equivalent time sampling, University of Applied Sciences FH Technikum Wien, 2016
REINHARD LERCH, P. D.-I: Elektrische Messtechnik Analoge, digitale und computergestuetzte Verfahren, vol. 6. Springer Vieweg, 2012