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.
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.