Here is the key difference between product and project manager:
Project manager works to achieve the defined goal, within specified timeframe and with predefined resources. So the key knowledge & skill here is around making optimal use of resources, time and effort for the sake of achieving this goal.
Product manager works to create a solution, usually with undefined scope, unclear timeframe and undefined budget for the purpose of maximising ROI. The key knowledge here is understanding of user and market needs and ability to make decisions which would create profit.
Everything else is extra. :)