You can think of antennas similar to your vision. 0dB would be considered you just as you with nothing artificial.
Now you decide that you would like to use a pair of binoculars to see further. The problem with binoculars is that your viewing range is not as large as you have with out them. However, binoculars are helpful, they let you see things that you couldn't see before. This is similar to lets say a 2.2dB antenna.
Now you decide you want to see even further, so you pull out a telescope. Again you are limiting the viewing angle, but it can be worth it in order to see further. This would be like a 7dB antenna.
Antennas are a little bit more complex, their baseline would be the ability to equally see in all direction (up, down, forward, backward, you name it) at the same time. This situation is called the isotropic antenna. This is where the 'i' in the dB comes from, and it is our baseline.
Going back to the example of binoculars and telescopes, antennas add a level of complexity to this because of this full 360* view that you start out with. You could have one antenna that has a pattern that still lets you see in-front, behind, to the left, and to the right but doesn't let you see above or below you. This type of antenna can have a gain because you cut out the above and below. Largely this would still be consider an omni-directional antenna because it still has a 360* view, but it wont be able to receive from directly above or below the antenna very well.
The basic concept that I am trying to get through is that gain can't just come out of no where, you have to sacrifice some part of the antenna pattern in order to give gain to another part of the antenna pattern.
So to your question of:
I presume any (2.4GHz) 2.2dBI antenna will yield similar, 100m, results
Not necessarily. Basically you could have a 2.2dBI antenna that has a really odd antenna pattern that causes you to have a lot of nulls in which you would have little range, while other areas might have a 100m range. To really find out you need to dig into the datasheet of the antennas.
It is worth noting that antenna manufactures will always do their best to try to make their antenna sound better than the competitors. This means they might measure their antenna gains in slightly different ways in order to get the biggest number possible. With any good antennas, you will be able to obtain proper antenna patterns.