Ammonia is tricky to test for, so the varying results with different kits is common. Make sure to exactly follow the kit directions as far as shaking vials, waiting 5 minutes etc. And try and make sure you perform the test the same way every time. From what I've heard, I'm not sure how good the Tetra tests are, but I've heard that mostly from the FW side so I can't recommend a better SW kit, I have the AP master kit for SW. I would probably trust your LFS's kit as they probably test enough water to go through the kits frequently and therefore aren't using old kits. These kits can and do go bad, and they really don't last that long, a year or two at most.
NH3 and NH4 are the same thing, for all intents and purposes. One is ammonia and the other ammonium, different forms of the same thing. Which one you have depends on the pH of the water. All the test kits are measuring the same thing, although there is more than one way to test which can give you different results if you use two kits with different methods. (for ammonia, either phenol or salicylate can be used, phenol is more common but more dangerous so the salicylate method is becoming more common now).
Ammonia is extremely volatile....if you had happened to wipe down your countertop or cleaned your windows with windex around when you did the test that could affect your resuts. When you aren't using your test kit, keep the vials full of RO water and rinse them out 2-3 times before and after the test. This helps keep things clean and minimizes the chance of contaminants.
A properly working RO system should remove all ammonia....I test nutrients in seawater for work and my check on our in-house RO system is my nutrient analyzer....it will pick up traces of ammonia getting through long before the meter on the RO system says the cartridges are bad. But when it's working, the ammonia is 0 (and with the machine I use, 0 is really 0! It's accurate to 2 decimal places, ie I can measure .02 ppm)
Hope this helps....happily your fish seem to be just fine, which is a good sign. Please let me know if there are any other questions I can answer, I do this for work so I understand it pretty well.