I made custom tags by designing them and printing onto iron-on transfer paper. Then I ironed them onto 1" ribbon and cut them out - they came out good enough for professionals, I think! See my post about a yoga bag below to see how mine are...
I saw them also on a craftster post somewhere, manipulate the search box for more detailed instructions.
My guess is that it's the modern equivalent. It was with the cloth that looks like the old-fashioned table cloths (with the red checkers). When I asked the girl about what it was, she first said it was vinyl. So then I asked what's the difference between vinyl and oilcloth and she corrected herself to say what I was buying was oilcloth.
So, I don't think it's "real" oilcloth, but it is waterproof and close to a thick fabric in thickness so it's pretty easy to sew (I used to use the clear plastic vinyl lined with a pretty fabric, how difficult that was!).
I made my first Amy Butler bag a few years ago - it was a bag to carry my yoga/pilates mat to classes. I made it from this turquoise AB fabric which I really liked.
I recently joined a yoga studio and have needed a bag (other than plastic grocery bags!) to carry my clothes. This is what I came up with (my first time working with oilcloth - I like it so much better than clear plastic vinyl! it sews amazingly well).
With an extra (waterproof) oilcloth section to divide my clothes from the day away from my yoga clothes: