Basically, it all boils down to this: A software engineer creates the software blueprints, a developer translates the ideas from paper to actual working code, and a coder is a developer who’s just getting started.
In terms of figuring out which path you’d like to follow for yourself, it depends on whether you enjoy working on the big picture or getting your hands dirty in the trenches. If you want to unleash your inner artist, then be a front-end developer. If you want to work with databases and APIs, be a back-end developer. If you want to make cool iPhone apps, be a mobile developer. Lastly, if you want to plan out how it all comes together, then being a software engineer might be in your future.
At the end of the day, however, the differences between all of these terms are relatively small, and people tend to use them interchangeably. Someone might refer to a developer as an engineer and vise versa. Ultimately whatever path you choose, software development is an exciting and challenging career. Few paths in life can be as rewarding and enjoyable as solving tough, challenging problems on a daily basis.