"Set" vs "collection" terminology: what is the difference?

Can someone tell me what is the difference in saying

$A$ is a set of even numbers

and

$X$ is a collection of even numbers

?

There is no difference between the two.

But, "set" has been the word that mathematicians have elected among its synonyms to describe the mathematical entity of a set/collection, as formalised in Zermelo-Fraenkel set theory. This entity can be used (in theory) to give a formal description of all of mathematics in the "language of sets".

In this respect, using "set" instead of "collection" will leave a more "mathematical" taste in the mouth of many readers.

But if history would have a quirk and "collection" would be the "mathematical" word, I'd have interchanged the two in this answer. It's a matter of definitions, and to some extent arbitrary.

Bottom line: Don't worry for now.