The one thing to understand first
A managed PostgreSQL service does not give you a different database. In almost every case you are still running the same community PostgreSQL engine you could install yourself — the provider has simply taken over the parts of running it that are tedious, risky, or easy to get wrong: provisioning hardware, configuring replication, taking backups, patching, and failing over. What you are buying is not the database; it is the operations.
Everything else about a managed offering — the pricing, the limitations, the lock-in — follows from one question: where is the line drawn between what the provider operates and what you still operate? That line is called the shared responsibility model, and learning to see it is the foundation of this whole pathway.
Control plane vs data plane
Every managed database is split in two. The data plane is the PostgreSQL process itself answering your SQL on a compute instance attached to storage. The control plane is the provider’s automation wrapped around it: the API and console that create instances, the agents that take snapshots, the health checks that trigger failover, the schedulers that apply minor-version patches in your maintenance window.