Technically its still the same computer. What you are talking about is setting up multiple boot volumes. In this case two distinct drives.
You could also create multiple partitions within one drive as well. The other approach is to setup multiple user accounts within the same running OS. And, the last method is to setup virtual machines (VM's) which runs within a single drive & partition volume, but allows one to run very different OS's concurrently. Apples BootCamp is an offshoot of a VM. Each of these setups have there benefits and disadvantages.
Here you are using the same OS just setting up different drives. You would then need to reboot your system holding down the Option key to switch between the boot drives.
You do have a few wrinkles here as you'll need to give up your optical drive for a 2nd drive carrier and you will also encounter a few known issues with the optical drives SATA port. First it does not support crash guard so you shouldn't use a HD that doesn't have it. The second issue is the SATA port speed is not a clean SATA III (6.0 Gb/s) signal, you'll need to install a fixed SATA II (3.0 Gb/s) drive either HD or SSD. So your 2nd drive will not be quite as fast as your primary drive (if you have a SSD presently installed).
The truth here is the dual drive is not the direction I would go! A single SSD should be able to support your needs. I suspect your real issue is your current SSD is running out of space so it appears to be running slower as it needs to work harder to reuse the limited free space it has. This is one of the reasons I strongly recommend you have at least 1/3 of the drive free and if you have a smaller SSD (128/256 GB) 1/2 free. If you don't have that much space maybe the better answer here is to upgrade your SSD to a larger unit or at least try cleaning off some space.
I should also point out if you run a SSD lean for free space you will wear it out sooner as the free space cells will be over used.
If you want to isolate what is exposed then you will just want to setup a second user account. Frankly, Most of my setups have a minimum of three user accounts: The system Admin account which the IT staff owns. The users primary account and a guest account. For my own systems I add another account for my banking needs, so it is fully isolated. And one more for when I'm shopping online. That way I've compartmentalize things so my information is protected and doesn't give away the gifts I give my girlfriend who is a bit of a snoop ;-}