Scarlet_3 :
I'm currently working on building a new computer and I'm planning on saving a little money on an SSD and an OS by just moving my SSD from my old computer to the new one. Is that something I can do since there will be different hardware components such as a different GPU and CPU?
Probably not. 2 consideration, Operation and Licensing.
Operation - Very often, what you are trying results in not booting. The only fix is a full reinstall
Licensing - Upon seeing the new hardware, it will almost certainly unactivate itself. Depending on what license you have (OEM or Retail), and where it came from, you might need to purchase a whole new OS.
Solution? Sell the old hardware with the old OS. Use those funds to buy new.