It's unrelated to either other than sharing the gig economy model. It's just another part of their Fulfillment Operations that relies on individuals with their own vehicles instead of a fleet.
I think that was clear from the context of the thread, where OP alluded to an in-house Uber, and I noted that the model was more similar to the local delivery services than to Uber per se.
Anyway: Amazon Flex drivers actually did handle delivery for Amazon Restaurants, which was a direct competitor to Uber Eats, DoorDash, GrubHub, Caviar, etc.