A QT should be used for new fish you buy, just to monitor them before adding to your main tank. That way if anything should happen, it dont affect your main tank and all other fish.
A hospital tank is for any fish that gets sick fish in your MAIN tank, but if you QT all new fish you should never need the Hospital tank.
Basically the same tank, just depends on the situation (is it a new fish, or a sick fish in the main tank?)
In your Qt/Hospital tank, it just needs to minimal---some pvc pipe (to hid in), a heater (if needed), a filter, etc. I only have a filter, some fake rock (instead of pvc pipe), and a heater.
I learned the hard way, even though a fish may look healthy for weeks at the LFS, it still is a good idea (though it sucks) to QT. HTH