Many years ago scientists thought they knew which bacteria were the important species in the nitrogen cycle.
These bacteria entered a dormant phase, and were easily packaged and shipped. They could even be carefully dried and incorporated on things like bio wheels and in dry flakes of barley.
The companies also found that there were other species, perhaps not directly associated with the nitrogen cycle, but always seemed to be present in the filter, and these also could be packaged and shipped.
Some of the bacteria in these old packages are:
Nitrosomonas europa (This one is in sea water tanks, but does not play a big role in fresh water tanks)
'faculative enzymes' (I have yet to figure out what that is!)
Heterotrophic bacteria (A group that is all around us, and can cause cloudy water, they reproduce so fast. Good bacteria, but not N-cycle bacteria. They will find the tank even if you do not add them.)
About 15 years ago a scientist working at Marineland actually identified the real species of bacteria that are responsible for changing the NO2 into NO3. A few years after that he identified the ammonia removing species. These were not so easily packaged, they do not enter a resting, dormant or spore stage. They need a certain minimum of oxygen and water to stay alive, and the right temperature.
Marineland started selling this as Bio Spira. Different formulas for fresh and salt water.
Other companies acquired the patent and started selling it, too. The scientist who figured it out left Marineland and is also selling his line of aquarium products.
Bio Spira is still available, but only the salt water version.
Fresh water versions include:
Tetra Safe Start
Dr. Tim's One and Only
Microbe Lift's Nite Out II
There may be others. The most direct way to tell is to read the ingredients. If it includes Nitrospira, that is the right stuff. If it says a bunch of stuff about 'helper bacteria', enzymes or Nitrosomonas or even worse Nitrobacter anything, this is the wrong product for the nitrogen cycle.
Another way to tell is to read the instructions:
If the package says you need to keep adding it, it is the wrong species. The wrong species do die out, so if you really wanted them you would have to keep adding them.
But the right species establish themselves on the surfaces in the filter and elsewhere and keep on reproducing. The only time you need to add them is if you add more fish, or something happens to the bacteria like getting killed by toxins.
Even if you do not add them from a bottle, these bacteria will find the tank. They are all around us, living in the soil, and pretty much any slightly damp surface.
Tanks that used the original (wrong species) would eventually cycle because the right bacteria would get going in there. Tanks that did not have any bacteria in a bottle added, right or wrong species would eventually cycle. Both of these set ups are using the fish-in cycle. Using fish as the supplier of ammonia, and moderating the level to keep the bacteria growing while not killing the fish. This method takes 6-8 weeks whether you use the wrong bacteria or no added bacteria. (Doesn't this suggest the wrong bacteria are not doing what they say it is supposed to do?)
The fishless cycle will cycle the tank as fast as 3 weeks even if you start with no bacteria. The right bacteria will find the tank and grow when conditions are right. It will also take 3 weeks if you add the wrong species. (See, the wrong species are not needed for nitrogen cycle.)
There are many other species of bacteria and other microorganisms that live in a mature aquarium. Mostly they decompose organic matter like fish waste, dead plant parts and fallen food. There are other species that do other things. If you are buying a bacteria product for these other purposes, do your research and find the best supplier of the right species or blend to do what you want. Remember, though, that microorganisms are all around us, and if you have the patience they will usually find the tank without you having to add stuff from a bottle.