I think the distinction Bluedevil is trying to make is you're going into this SaaS app with no intention of it being hugely profitable or successful. You're scratching an itch and if other people decide to pay you to help scratch their itch as well, then that's just a sweet bonus.
In contrast, a business would be going in with the intention of the service/app being successful (profitable or popular). Maybe hobby isn't the best way to describe it, but I agree your way of looking at things is closer to a hobby then a business.
In my book If you don't enjoy doing it not a hobby. If you care about ROI, and profit it is a business.
For me weather something is a business or a hobby has more to do with outlook than anything else. A few lucky people have insanely profitable, and scalable hobbies with 1000s of employees, and plenty of kids are struggling to keep their lawn mowing biz afloat so they can afford a new video game.
Over the years I've been told that company I founded 8 years ago, and has been my and several other peoples's day job ever since, is a hobby for many reasons, including not enough W2 employees, revenue and so on. Which, even though these things were said to prop up the speakers egos, made me think on the topic - and this is what I've come up with.
In contrast, a business would be going in with the intention of the service/app being successful (profitable or popular). Maybe hobby isn't the best way to describe it, but I agree your way of looking at things is closer to a hobby then a business.