Normal backwardation compares futures price with expected future spot, while backwardation uses the futures price with the current spot price, same for contango.
The idea is if the expected future spot is higher than the actual futures contract price, you have normal backwardation. There has to be a reason for a hedger to enter a contact, why would I take the other side of the contract and have no expected profit. So that difference between the expected futures price and the futures contract is to “compensate” the counterparty to take the risk. I haven’t revisited this topic so someone may want to chime in!