A system camera is a camera that is part of a system, most importantly has exchangeable lenses, but also possibly a flash system, exchangeable sensor, and other associated extras.
A compact camera is a camera that is NOT part of any system and is complete on its own, including coming with a fixed lens.
A point and shoot is a compact camera that can be pointed and shot without further ado, meaning it doesnt have much in respect to photographic controls and doesnt need much photographic knowledge. There are no system cameras that are this simple, because that wouldnt make much sense. You can use most system cameras as a point and shoot, though, since they have the so-called "green mode" - i.e. AUTO - which does everything just like a P&S.
The term "mirrorless" usually refers to an EVF based mirrorless camera, the new competition to the previously (and in fact still) dominant DSLRs. There are a ton of pre-SLR camera designs that are technically also "mirrorless" - large format cameras, rangefinders, twin lens reflex cameras, etc.
Back in film times there have been SLRs which have been compact cameras. These no longer exist.