My test for fire ants is to hold one end of a stick while you put the other into the top of the mound. If they come charging right up the stick, they're fire ants. Don't let them do that on your leg - or maybe you already know that.
There are lots of homegrown solutions for fire ants: boiling water, etc. etc. After you're tried them all, you'll find Amdro works. You only need to kill the queen but she's not easy to reach. The workers take the Amdro to the queen. Some approaches just annoy them so they pack up and move, but not far enough.
If they're not fire ants, I'd vote for live and let live.