These are measuring two different things, so the different results aren't surprising.
The first thing you showed is reflecting memory consumed by processes running in user space alone.
Adrenalin is showing what the total "in use" memory is, and it should more or less match up with what task manager reflects... if you're looking in the correct place.
This is your total system memory use, and specifically, it's the one I have denoted in Green. The one denoted in Orange is a further breakdown and is counting "in use" memory, but it does not include what is on the "modified page list", which is what little sliver of memory to the right is. That does count towards your total memory use, hence it is added to the "in use" value to get the larger value in the Green box. If I were hovering that spot at the time I took the picture, it would show much memory is being used for that, and it will likely have shown something just shy of 300 MB, which is the difference between the 7.7 GB and 8 GB shown.
This is why I asked for the two specific task manager screen shots, because if it wasn't showing up in user space, I wanted to see if VRAM and system RAM were both full, and perhaps if there was a clue as to why (a very high paged or non-paged amount, for example, which can be common if the leak is occurring at the driver level). You should never be looking at the process list when trying to figure out how much total memory is used. That won't give you the correct answer. That may be useful to seeing if an individual process in user space is claiming all of that memory, but your screenshot didn't indicate this, which is why I suspected it was outside user space. If trying different drivers stopped the leak, then that would make sense. Something was causing VRAM to fill, and when that was exhausted, it started spilling over into system RAM.