Hackerspace is the original term, but some places call themselves Makerspaces instead because “hacker” has a negative connotation with the common populace. A hack, in the original sense is almost equivalent to ‘redneck engineering’. It’s a non-formal environment, probably doing non-standard things…thus a hack.
They are generally found around larger cities, universities, etc – there’s not enough population otherwise to keep them running as they’re generally member-funded, and they still gotta pay things like rent.
Fablabs are similar, but corporate-owned and you’re expected to use tools and GTFO; not stick around and be social.