Like the name suggest this is a lens mount adapter system.
So instead of Tamron making the same lens with different lens mounts it instead made the same lens which can be fitted with the mount that you want and it support.
Very smart system which I see as a win both for the customer and the manufacturer.
The adaptall & adaptall-2 are the latest system like this from Tamron but thay also have two older once.

T2
Adapt-A-Matic
Adaptall
Adaptall-2

These are all for older manual focus lense and I have so far tested the latest adaptall-2 with a Pentax K mount.
And can't say that I notice any difference between this system and a fixed mount in practical use.
These are very well made and fits like a glove but there might be some adapters that are better than others.
Removing and mounting the adapter is however not as easy as changing the lens on you camera.
This is a little fiddly but it also something you usually don't do very often if ever.

This system support a ton of different mounts and can be used with next to all SLR's, old or new.
But this is a older mechanical system so some restrictions with newer electronically controlled mount can be found.
Like the Canon EOS for example where the aperture is electronically controlled and the will work as a Manual aperture (preset).
Here you can find a wiki page about Tamron and info about there different adapter systems etc.




To what I have read the Adaptall 1 & 2 are the same system but the second ver supports more advanced mounts.
Like the Pentax-A which supports auto aperture for example.
You can apparently not use a lens made for ver 1 with a ver 2 adapter and vice versa.
At least not in most cases but read on a forum however that some of the simpler mounts like M42 has the same adapter for both of the versions.

There would be nice if all manufacturer came together and made a universal mount so you could use any lens on any camera.
One could dream but we will probably never see that in a consumer society.
But the is a really smart solution for that problem and it works really well.
Tamron have unfortunately not made any system like this for more modern AF lenses.
And I would guess that it would be very hard to support all the newer mounts functions etc.