No, you miss the point: what is the difference between a hobby and a job? You are doing something either way. I'm not the only person who likes my job. I'm not the only person with a hobby that sometimes gets frustrated with something in the hobby.

The freedom/free time part is obviously the distinction!

Sure, but why is that important enough to make in the first place?

Note if you don't have a background in philosophy you probably can't answer this. If you do the answer will take many pages

Note if you can’t understand why the distinction matters in general, in practice, and to many people then you might be unhealthily privileged and should try to get some perspective.