To expand a little on what Tom said about drawing skills:
1. The drawing skills required to make something that works as a prototype for a producer, literally takes about 2 days of Youtube fanboyism to learn. And it looks awful.
2. If you want to get something that looks great yourself (e.g. for a downloadable indie title on your own website), you can literally get someone to do the artwork for you.
As for game developers, that's just anyone who literally and physically makes the software. In big companies, nobody is just a "game developer", cause that's just a general term. Everyone have specific roles. In that case, they call the big boss the Lead Developer, The one who coordinates with Designers or even Lead Designers of specific disciplines (depending on the team structure).
The disciplines of game design include:
* World Design
* System Design
* Content Design
* Game Writing
* Level Design
* User Interface Design
* Audio Design
(ref. Wikipedia: http://en.wikipedia.org/wiki/Video_game_designer#Game_designer)
As an indie developer, however, you're doing most or all of that work yourself. So you're "The Developer", and sometimes even the producer and distributor to boot (if you're making your work available for download on your own website). If you're really good, the marketing can happen through fans themselves simply enjoying your game and sharing that experience with their fellows. Kinda interesting how Mojang haven't spent a single dime on marketing Minecraft.