Issues with some games stuttering on 4TB hard drive

TL;DR : You need more RAM.

Whenever a game needs more RAM space than available, it will reserve what it needs from the hard drive. This is the definition of Virtual Memory. The thing is, because the some-kind-of-needed-resource is located on the drive rather than the RAM (aka where it's supposed to be), the access is much slower than straight from the RAM (in other words, the CPU needs more time to retrieve data from the hard drive than when it's in the RAM) hence the lag / the freeze. Then comes the counterproductive part of having a large storage, the CPU needs to travel throughout the whole 4 TB to get that data every time it needs to. Think about it as if you needed to wander through a huge parking lot whenever you forgot something in your car. This is why your 2 TB storage looks to be comparing better to its double-sized other hard drive : you spend less time looking for your car in a 200-car parking lot than in a 500-car one.

It is also important to know that not the full 4 GB of RAM is allocated to the game, since the OS needs material to run with (I guess 2 GB for Windows, that's already half of your memory available and you did almost nothing yet), so I would definitely recommend getting some more RAM (there are 2, 3, 4 GB sticks, you would easily get waaay up into 16 GB, which is more than enough, since games alone do not require that staggering amount of RAM anyways).