Delivery
Delivery is the handoff at the far end. Inspect the car before you sign the release. Note new damage on the delivery report first. Paying the balance and signing a blank form are separate acts.
Delivery is the carrier giving the car back. The person who receives it may be you or someone you named. That person should walk the car against the origin condition report, in enough light to see the panels. New marks go on the delivery copy before the signature.
The order of the last ten minutes
Inspect. Photograph. Write exceptions on the bill of lading. Then sign. Then pay the balance if the contract says it is due to this driver and the amount matches. Signing a clean release and then finding a dent in the driveway is a harder claim. If the light is bad, write that down.
How it differs from pickup
Pickup records the car the carrier accepted. Delivery records the car it returned. The claim is the difference, inside the claim window. RideShipper is not at the curb and does not sign the release. If nobody on your side can be there, name a person in advance and tell them not to sign a blank page.