I am a bit confused about the difference between variation $\delta u$ and differential $du$.
I saw them in terms of minimizing a functional. The way the variation operates seems very similar to derivatives (chain-rule and so on).
I have a hunch that variations talk about small deviations in function (throughout its domain) whereas differentials talk about small changes in discrete quantity. Am I right about this? An answer in Layman's terms would be much appreciated.
In simplistic terms, a differential relates to the increase in the value of a function, an object taking a scalar as argument and returning a scalar, for a "small" variation in the independent variable. A variation relates to the increase in the value of a functional, and object taking a function as argument and returning a scalar, for a small variation in the argument function. Your intuition seems correct, although I am not so sure about the reference to "discrete quantity".