There are three different ways to design a Yagi antenna with three or four elements.
One is gain, a yagi antenna with peak gain in the forward direction tends to have a pretty significant secondary lobe facing the opposite direction. I actually know a ham that thought his antenna was pointed the other way, and literally talked the world on this secondary lobe, but that is another story for another time.
The next method of tuning a yagi is for front to back ratio. This is essentially maximizing the difference between the power going to the front compared to the power coming off the back, and sides as well. This lessens interference from other stations and sources in directions other than what you are pointing. In time, more experienced people tend to move towards this layout as often blocking unwanted interference can have more of an effect on your ability to make and maintain contacts than the extra little bit of gain out of the front will get you.
And third, it is possible to have a natural, (without the need of a matching circuit) coax match at the feed-point of the antenna.
What the design goals of the antennas listed above are I don't know, you would likely have to talk to the people who designed said antennas.
Also, assume you won't get the gain figures that are listed. While I'm sure it is possible to get said gain figures, it is very unlikely that your installation, wherever it may be, will get you the same gain. Its possible to get a higher amount of gain, but more likely you will end up with a lower amount of gain.
Also, those charts and listed specifications are part of marketing, and marketing doesn't exist to get you accurate information, its there to convince you to give said company your hard earned money, so be aware of that when making a decision.
And finally, and this is more of a pet peeve than anything, but,,, Antennas will only transmit the amount of power sent to them, they don't multiply it in any way. What they actually do is focus it in some certain (hopefully beneficial) direction(s). The more focused the signal, the higher the gain. That is all.
Hope this helps.
The DB