Its way of being obtained is different. You can buy PokeBalls immediately and in bulk from most any PokeMart, but to obtain Premier Balls, you have to buy at least 10 or more PokeBalls, and Premier Balls are given to you as a bonus.
You also must have a Poke Ball in your bag to evolve Nincada into Shedinja. Attempting to use a Premier Ball will fail. There are also different in-game trades across generations, where Poke Balls can be traded for other types of balls. Attempting to trade a Premier Ball will cancel the trades.
Hope I helped!