A hospital tank should be set up with clean sterile water not tank water. You can make the parameters the same as your tank but it is better to be 0s for ammonia, nitrite and nitrate. The tank can be set up the day before the fish are to be placed in it because the more sterile it is, the better off the fish will be. Also, some medications will interact with biological waste so you really want the tank clean.
A quarantine tank is a whole other story. That is where you will place a new or healing fish in order for it to recuperate or adjust. That needs to be set up and maintained more closely to your main tank.
Hope this helps.