Planetscale is MySQL that is automatically sharded and proxied with a system called Vitess to scale horizontally. Because it's real MySQL, most functionality still works without the operations overhead.

Neon is Postgres that has a surgically enhanced data layer that reads from a distributed set of nodes and object storage, but is still a single Postgres instance that's started and stopped on-demand and not automatically sharded. Because it's real Postgres, all functionality works including extensions without dealing with issues from sharded datasets, but also without the horizontally scalability and instant start (so far). However because the data layer is improved, the actual compute node is much more efficient in both startup and processing so it works well in many scenarios.

CockroachDB is a proprietary distributed database built to Postgres wire/data protocol with natively separated storage and compute. Their serverless plan also starts and stops instances as traffic comes in but with fast startup because of their specific architecture. Because it's not real Postgres though, there's a good bit of missing functionality.

Thank you. This is helpful.