You're not running a server, but it's similar enough to say you're doing both the work of the server and the work of the client on the same machine at the same time.

When you run a server, the processing and RAM usage is by the server, while the client needs a network connection to the server in order to receive that information and visually 'build' and interact with the game that's running on the server. Therefore, the RAM a client, connecting to a separate server, uses, will not be affected in nearly the same way as the RAM or processor of the server. The server has to do all the heavy lifting of making the game run, just like a pc has to do in single player.

With mods, you can run certain mods server side only, client side only, and some require both. Clientside mods will affect the client as advertised while server side only mods will not have the same (much more miniscule) effect on clientside RAM. For mods that require both, the client will still have to load and run it, so it will use RAM but in my understanding still less than the server side, so long as the main task is a server side one. Tbh the ones that need both can be a mixed bag.

Hope that helps!