A set implies a formal, identifiable relationship between the items. That's why the word set is used in mathematics. Number sets. The set of real numbers, for example. When used for THINGS, a set of tools, the implication is that they all belong together in that category. A set of tools would not include toys. Sets are not defined by a person. They are defined by the category of thing.
A collection is just a group of things that do not necessarily have formal unifying characteristics but that have been brought together by a person, the "collector", either formally ("He is a stamp collector") or informally ("Look at that collection of junk on their porch"). In the second example, someone has collected (grouped together) the junk and put it on the porch.
So, using those definitions, we might get:
I have a set of Civil War stamps in my collection.
I have a collection of stamps. [I collected them]
I have a set of [dog, cat, animal, outdoor] sounds that we can use. [cat, dog, animal and outdoor make them belong together]
I have a collection of sounds that we can use. [I collected the sounds.]
I have a set of Iron Age weapons. [the all come from the Iron Age]
I have a collection of weapons. [I collected the weapons. I put grouped them together.