Actually, the wires that you have are thus:
Big fat gnarly wire is the main power wire, as you surmised. It comes directly from the battery. It provides power to the solenoid, not to the starter though (well, ultimately it gets to the starter ... I'll explain). There are two parts to the starter (in most vehicles). The larger part which actually attaches to the engine is the starter motor. This, as the name implies, is the part which actually gets the engine to spin. The smaller part is called the solenoid. The solenoid has two purposes. Its first job is to move the starter gear into position so it will contact the engine flywheel (or flexplate depending on type of transmission). The second thing it does is to act as a relay to energize the starter motor.
The other two wires is where your understanding goes astray. One of these wires provides power to the solenoid to energize it. This wire gets energized when you turn the key switch from the "on" position to the "start" position. (I'm pretty sure on this next part ... someone correct me if I'm wrong ...) The second wire you are looking at provides full 12v power to the ignition system (coil) during starting. This makes it so the spark plugs provide a little extra umph during that process and hopefully allows your engine to start quicker. It pulls this power from the energizer wire as it is only needed during starting, so is a convenient place to have it.
There isn't a ground wire going to the starter. It utilizes the the metal connection of the starter case attached to the engine itself as the ground. The engine is grounded to the body and usually directly to the battery.