(Continuous|Quantitative) variable is a numerical variable that can be any of an infinite range of values.
Any-time you measure a variable that can only be measured in discrete values, you are using a variable that is not truly continuous.
A continuous variable is a variable where the cumulative distribution function is continuous everywhere. There are no “gaps”,
Continuous random variables almost never take an exact prescribed value as discrete variable does.
Illustration Continuous vs Discrete: A Geneva drive is a gear mechanism that translates a continuous rotation into a discrete motion.