How to understand the PostgreSQL discrepancy between connection pool recommendation ((2 * n_cores) + n_disks) and support for 100s of connections?

From PostgreSQL docs:

• Number of Database Connections -> How to Find the Optimal Database Connection Pool Size

  for optimal throughput the number of active connections should be
  somewhere near ((core_count * 2) + effective_spindle_count)

• Tuning Your PostgreSQL Server -> max_connections

  Generally, PostgreSQL on good hardware can support a few hundred
  connections.

For me – not an experienced DBA – there’s a discrepancy somewhere in here, especially looking at the offerings of some DB-as-a-Service providers.

For example, at this time Amazon RDS’s largest machine (db.r3.8xlarge) has 32 vCPUs, which according to the first formula would perhaps manage to run optimally with 100 connections in the pool, given many disks. Wouldn’t it though run very badly with the “few hundred connections” from the second formula?

Even more extreme is the discrepancy for another DBaaS provider, who proposes a 2 core server with 500 concurrent connections. How could this possibly work well?

If I’m misunderstanding something, please let me know. Many thanks!