I have a rather sad looking specimen of either this "Maidenhair fern"
Southern Maidenhair Fern (Adiantum capillus-veneris)
or this one:
Himalayan Maidenhair Fern (Adiantum venustum)

Given that mine came from Wal-mart (sorry, it's so sad looking that there's not much point in trying to take a photo, but it IS still alive. I think.), I'm guessing that it's probably the first one. But they look very similar to me. Any hints on how to differentiate them?

At this point, if the plant you got from Walmart is still small, I would wait on naming it until it is more mature. As with most plants, stems and leaves change as the plant matures and the adult leaves(fronds for ferns, so to speak) are produced. By then you should be able to tell the difference between the two. Also look at the how the frond is divided between the two and the leaf shape. I'm not sure if the spore cases that appear underneath are in different configuration or not, since I've never seen them. This is about as much as I can offer. But until the mature fronds are produced on your rescue plant, I wouldn't make up your mind on naming it.

No, this isn't a young plant, I've had it for 3 or 4 years, it's just looking very sad right now, lost a lot of foliage, but appears to be trying to come back. I should have re-potted it much sooner.

Ah, with the help of your suggestion, Kurt, I answered my own question. Looking very closely at the individual leaves on the fronds (and with many thanks to the members who posted such nice clear photos!), it is most definitely Adiantum capillis-veneris. The individual leaves have a sort of scalloped edge, where the venustum is rounder with a sort of saw-tooth edge.

I'm very glad that you figured out what you had. Sometimes, it's never easy to know, if you can't remember what it was or even where you got it or you lost the name tag. I know, I've done it before myself. I'm just glad I was of some help to you.

Good growing to you!
Kurt

And it's still alive! (so far ) Still not happy, but not quite dead.

The one thing that I learned about Adiantums is that they like humidity and coolness, not cold, just cool. They do very very well in Terrariums because of the humidity, at least for those that are tropical. The northern outdoor types still like their humidity and cool shade to grow well. I always thought they were very pretty and delicate looking. I've thought of getting the Northern Maiden Hair fern because of it's unusual frond configuration and it's beauty. I'm glad that your fern is doing so very well.

Good growing Woofie

I wonder if it would help to put a little container of water in the pot. Couldn't hurt.