I'm thoroughly confused as to why a static shock on my laptop will effect my desktop. I don't notice anything odd on either machine, they're both working without problem.
Understand what this current is. You have created charges on both sides of your shoes. The discharge is a current path that leaves the finger, passes through items (ie laptop) to connect to charges beneath your feet. Things you consider not conductive (ie floor) actually are conductive. Just not conductive enough that we call it non-conductive to AC electricity. But conductive enough for static electricity.
So, how did that current get from your finger tip to beneath your shoes? One possible path is into the laptop, out via the safety ground wire, over to the other electric socket, into the desktop's chassis, into the floor, and connecting to those charges.
Well, that would not explain the noise. However some minor variation in that path might.
One known fact is that an electrical connection is made from your finger to charges beneath your shoes. How it gets there and how it might affect computers is a mystery that only you have sufficient information to answer.
BTW, static electric discharges are a superb diagnostic tool. As may become obvious with further discussion.