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.