Diferent company has different title system. In general, PM is just a coordinator for the product or project. For the entry level, there is not too much difference between engineer or PM. After Project/Product manager, you may be promoted to Potfolio management. If you are good engouth, you may also be promoted to Manager of PM who has direct report. Engineer also has its own track to Architect/ lead and etc. Anyway PM is just a title, not a real manager in other industry who has direct report. It's like manager/avp/vp in bank system.
Pick based on what you like and what you good at. If you are good with inter-persona skills and like to do money and time tracking for others, then PM is the choice. Otherwise starts with engineer which may have lots of potential too. Don't forget most IT startup owners are tech-savvy themselves.