As PE said, all thiosulfate fixers can bleach the image if used too strong (time, concentration), sodium being less active than ammonium.
There are three two-place variables in currently available fixers: pH, thiosulfate type, and hardening agent. All variations exist, so that's a total of 2 at the power of 3 = 8 possible fixers.
* pH: alkaline or acid. Acid is more readily available. Alkaline washes off more easily
* Thiosulfate: Sodium or Ammonium.The differing uses between sodium and ammonium are based on the type of silver salts you need to fix away. Modern emulsions for both film and paper contain silver iodide, which really needs ammonium thio fixer.
* Hardener: old emulsions were not much hardened, so an extra hardening step in the fixer was useful. Not necessary with modern films/papers.
So you can have:
- Acid sodium w/ hardener
- Acid sodium w/out hardener
- Acid ammonium w/ hardener
- Acid ammonium w/out hardener
- Alkaline sodium w/ hardener
- Alkaline sodium w/out hardener
- Alkaline ammonium w/ hardener
- Alkaline ammonium w/out hardener
I use Ilford rapid fix (non-hardening, ammonium thio, acid) simply because it's available at my corner photo store, and because it's the best for my purposes I can find on the shelves over here. The other choice is Kodak Kodafix (liquid hardening acid ammonium), and Kodak plain fixer (powder hardening sodium thio), none of which meet my needs: I don't need hardener or sodium thio (I use modern films and papers only).
I'm just not that into buying liquid fixer by mail, so I stick with what I can find.