Here’s my analogy:

A project manager makes sure the trains run on time.

A product manager sets the destination and the places you call at on the journey.

Both roles are important.

As complexity and dependencies increase, say in a bigger company, it helps all involved if you have different individuals performing these roles.

Side note:

Some companies have program managers instead of project managers.

‘Programs’ are usually bigger than an individual project but for simplicity, you could use the terms interchangeably here.