As shown near the end of this 5 minute video when Galileo rolled balls down a ramp he noticed that the increase of speed was continuous, however, he had to measure the discrete position of the ball at discrete points of time:
https://youtu.be/ZBr8Q2ROX9s
Galileo knew that position, time, and speed have properties that we now refer to as "continuous variables" however he could only take discrete measurements and he could only apply the math of finite differences. Today we might say that Galileo normalized values by defining time = 1 and position = 1 for a particular experiment and then he took more samples or discrete measurements of time when the position = 4, position = 9, position = 16, etc.
Today we automate sensor measurements using sample and hold circuits and other methods to convert continuous variables into discrete time representations.
Discrete models are considered to be approximate representations of continuous systems. The Calculus was invented to develop exact representations of some continuous systems. We can easily convert Galileo's discrete model for a ball rolling down a ramp into a continuous model with an exact solution using the methods developed that we call the Calculus. However we cannot measure the time or speed of a ball rolling down a ramp without assigning a discrete number value and unit of measure. Therefore our measurements have limitations as discrete events with limits of accuracy and precision.
Digital values are representations of discrete number values in terms of a data scheme such as integer format or floating point arithmetic. When taken from sensors these measurements are called "samples". Ironically the models applied in modern digital computers are only more sophisticated approximations using the math of finite differences known to Galileo.