I wrote out a script, and when I hit play, the script just disappears from where it is. I go into ServerScriptService (where the script is) and nothing is there. Is this a glitch with studio or something on my end?
I shall give you the answer you're looking for.
The client is what we play through on each game we decide to play. Some spots such as ServerScriptService & ServerStorage can not be accessed by the Client. Only the server can access those storage files.
The server is the item that receives the information from the client and replicates that to other clients. The server can access everything and anything that is within it's server.
The answer is quite simple, the Client can not see the said items in ServerScriptService so you will not be able to access or see the scripts through the said Client. You can only see it through the Server and there isn't a way to do that while playing the game truly. You can switch between the Server side and Client side in studios for your games but you need to understand studios to do something like that.
If you're putting your script in ServerScriptService, you'd be wise to have a event to fire to that said script that will do something when the event is called.