Both 揃う and 集める include objects or living being coming together at one location, but there's an important difference:
- 集（め・ま)る is more or less a neutral collection
- 揃う on the other hand includes a connotation of the collection being
sufficient or complete
You can 集める the pieces of a puzzle and end up with 1000 out of 1500, with 500 missing; but if the pieces of a puzzle 揃う, you've got all you need to complete the puzzle.
If there's a real difference between two words A and B, I think it's important to have a sentence with both words, such that A is true and B is not. So to illustrate, here's a short sentence using both verbs:
[members of an online community want to meet in real life]
It won't be possible for all of us to gather, but it would be nice if we could get 20-30 people with the regular users.
If people gather at a train station, they're just an unordered group of many individuals. But if all members of the family come together, they're complete.
A few more examples to illustrate the difference:
揃う: gathered, and that's sufficient
集まる: gathered, but not yet enough