Postgres RDS is indeed different, yes it runs on EBS, but the Aurora in a sense isn't truly Postgres. What they've done is forked away from vanilla Postgres and tweaked the storage layer to work on the block based storage they've built just for it. It's why you see it advertised at "Postgres compatible" vs. just being will standard Postgres.

This article is definitely an interesting one as it highlights some of those trade-offs that they now need to account for.

The key difference between "classic" RDS and Aurora is that classic RDS really only automated the control plane. That is, RDS spins up an EC2 instance (or two, for multi-AZ) on your behalf, attaches an EBS volume of the appropriate specs, installs Postgres, sets up security and backups and replication etc.

Under classic RDS, when your application makes a SQL connection (the data plane) it's talking to a more or less stock Postgres instance, the same as you would have if you ran it locally.

Aurora, on the other hand, is involved in both the control plane and data plane. Your SQL connection is to a Postgres instance that's been forked/modified to work within Aurora.