However it's not a business I will be
running. It's more like getting paid
If you ask anyone from the finance office they will call this argument bullshit. Like that - and send you a fine.
If you do something to make money it is per definition a business. Point. It may not be a company, but it is a business. Saying "hey, it is more like helping people" - well, seriously, Honda is also not a business. They basically help people to get cars etc.
Let's say I develop an app for another
person or a company, is it OK for them
to pay me through a check to my name?
Depends on legislation. Which country you said you are in? Oh, you did not say. See, "taxes" is not something that is globally the same. Depending on legislation it may be legal (you have to declare as income), legal (they have to pay taxes on top what they pay you) or illegal.
My "work" is basically informal.
Ah - no. It is work for hire. Or it is selling software. Whatever it is, if you do it regularly and a lot (not a single check) you will get into arguments with the tax office about that not being a business. Arguments that will cost you a LOT.
And dont forget to put that income on your tax declaration. Informal or not - it is income.