What's the difference between Nitrite and Nitrate and do you need seperate test kits for each of them?

Yes you do, nitrites are poisonous to goldfish at the 1.ppm range this comes after the ammonia in the tank. the bio bugs change the ammonia to nitrites both in fact are quite harmful to the fish.

nitrates are the last part of the cycle and can really only harm the fish at higher levels like 40-50ppms..... to get rid of this you need to do water changes or to help reduce them live plants. But over all water changes is the only way to get rid of them.

most test kits only come with Ph, ammonia, nitrites and Kg or Gh. the nitrates need to be bought separate