To begin, first understand how product management came to be. While it has its deep-seeded roots that go all the way back to Hewlett and Packard - the most important thing to remember is that product management broke OFF from project management. Why? Because you focus on different things.
Project management involves things such as scheduling, managing resources, and budgetting, to name a few.
As a product manager, you'll be focusing on giving your product a vision and direction. You'll be focusing on what problems to solve and how you're going to get there. Drop the dates, and focus instead on time-horizons.
Think of it this way - you're the captain of the ship (or at least the Commanding Officer) - but you're certainly not managing the rowers, you're just telling them where to go.