90% of indie devs I know want to do the latter because sharing their game/art/vision and seeing people experience it is the goal. Totally fine to do gamedev as a hobby but that's something discretely different from being an independent game developer.
You're right though that I may not count as a real indie game developer since I do it purely for fun.
Nuclear Throne is something I'd consider "shipped". It's polished, the design is solid and it's currently sustaining Vlambeer commercially. Compare that to their prototype(wasteland) and you'd get an idea on the difference(also ~2 years dev time if I recall correctly).
[edit]
I can also highly recommend watching anything from Rami Ismail of Vlambeer. He's brutally honest about the realities of being an indie developer and the mindset you need to be successful.
[1] https://vlambeer.itch.io/wasteland-kings
[2] http://store.steampowered.com/app/242680/Nuclear_Throne/