What is the role of a product manager in any organisation? And how is it different from Project manager?

A product manager is the person who identifies the customer need and the larger business objectives that a product or feature will fulfill, articulates what success looks like for a product, and rallies a team to turn that vision into a reality.

A project manager has a very clear and specific customer or goal. They lead teams which are internal facing focussed on single customer. While Product managers leads team building customer facing products.