I can give the basics, but kind of a lot of typing, even for me, to give full explanation.
Virtually all "ammonia test" you read about in pond forums are a "Total Ammonia" test, ammonia (NH3) and ammonium (NH4+).
These 2 chemicals do something interesting. As pH and/or temp increases NH4+ converts into NH3. As pH and temp decreases NH3 converts into NH4+. So with a Total Ammonia reading AND the pH AND water temp you can calculate the amounts of NH3 and NH4+.
This is all important because only NH3 (ammonia) is actually harmful to fish, while NH4+ (ammonium) is safe (as long as pH and temp don't change).
Why this is important...seen this many times in pond forums. "Experts" will tell new pond keepers to screw with pH and never mention ammonia. New person increases pH and fish start getting into trouble and none (and they do like to pile on) of the "experts" know why. Many of the things tossed into the pond then make ammonia testing difficult so more confusion, more crap tossed into the pond. Finger generally gets pointed at the new person..."they must have done something wrong. I raised pH in my pond and fish were fine
". A person does one thing one time and thinks it's proof of something. Cornerstone of internet thinking.
The ammonia ammonium relationship in most ponds isn't really super important in many cases especially when the pond keeper is serious about bio filtering. This is because the bacteria (and other critters) that convert ammonia and ammonium consume KH so these pond owners normally keep KH high which keeps pH high and stable. Once you get above say 8.5 pH then NH3 (ammonia) is going to be a big part of Total Ammonia so that test can be good enough. I've seen pond keepers who use KH measurements to understand how their bio filters are working, but that should only be an indicator imo.
Sometimes in the spring people test Total Ammonia, get a highish result, freak out and dump all kinds of stuff into the pond causing serious problems when there never was an actual problem because water temp was so low that harmful NH3 was actually low.
With proper bio filtering both NH3 and NH4+ is very low. (we say zero but that's not actually possible). Knowing the relationship between NH3, NH4+, pH and temp helps understanding which leads to achieving the goal. And also test how much actual bio conversion a pond has. For example, say you have 3 barrels of bio media...is that 10x more than you need and you're safe or do you have just enough and tomorrow ammonia will start creeping up? In both cases a zero ammonia reading doesn't tell you. So you can take one barrel off line and measure ammonia over a period. If ammonia creeps up you know you don't have 10x. A serious person can keep doing this until they have a good idea of how much ammonia their filters can handle roughly. Understanding NH3, NH4+, pH and temp means you can do this testing safer, so NH4+ creeps up and not NH3.
Of course all this has little use in Water Gardens where bio filter isn't normally needed. This stuff is what owners with Koi ponds packed with large fish have to do to keep the herd alive. Most Water Garden keepers who add something they refer to as a bio filter just think it looks cool and assume it's way good.