Project management is "create, maintain and drive the ticking off of a to-do list being done by multiple people inside/outside company to achieve a goal" - e.g. "move from Dynamics CRM to Oracle CRM", and it cares a lot about setting exact timelines and ticking off when tasks are done. Most quality control or creative input is done elsewhere.

Product management is "understand a market and customers to create or improve a product, prioritising features to feed to teams to deliver based on some metric (e.g. "creates most new sales" or "slowly improves the lives of existing customers without breaking anything"), and is often highly involved in quality (and perceived quality matters such as UX) and is fairly creative, as it decides what features go into the product.

Product companies tend to have more product managers and less project managers (they’re usually called something else, like simply software engineering managers or tech leads who have take on the project management duties).

Traditional enterprises and software consultancies tend to be organized around projects rather than user-centric products and their features, so they will more often have project managers instead. The product responsibility in turn tends to become more ad hoc, sometimes with someone assigned as a “product owner” outside their regular title.

(My personal view: if a company has project managers and product owners, that’s a sign that it’s probably not the place for me.)

Product Managers decide what they want the Project Managers to manage.

eg: "New Feature X" or "New Product Y" or...

Project Managers are about estimates and critical paths and resolving bottlenecks and competition for resources.

Product Managers are about features and sales and product roadmaps and marketing campaigns etc.