The value of both is the same, but the manner of use is different. If you have AppSumo Credits, you cannot claim products using the normal checkout methods. You have to choose your products from a special credit store. You can also see your credit balance from the same place.
If you have the AppSumo Passcode, you are given a special pass code just for your use. You can use your code in the coupon code field when you checkout using our normal checkout process. To start choosing your products, go here.