Learn English – To do a backup x to make a backup

I'm afraid the only general distinction is the one you have already named: do = perform and make = create.

But that is no more than a general tendency; as your examples show, in any specific instance either or both may be relevant, and at some point in the history of the language one has earned more favour than the other.

It's often possible to see a reason why one is used rather than the other in a particular situation, and that's useful for remembering which one is used; but it is of no value in predicting which one is used when you encounter a new situation. For instance:

You complete your homework assignments, which included writing down the answers to a series of questions. It seems that should be 'making' your homework, but in fact the proper phrase is doing your homework. You might remember this by considering that sometimes your homework doesn't call for you to 'make' anything: it might be reading a chapter in your textbook. The important thing is you did the tasks that were assigned.

You agree to act as the fourth person in a game of contract bridge. You would think this would call for 'do', since you are performing a role; but in fact you make a fourth. You can remember this by noting that what you are doing is “making” a complete table of players—would that have occurred to you before you encountered the phrase?

There's just no telling. You have to learn the right term case by case.

Here's a sort of popular vote by internet usage: Google hits for "rightdoing" = 75,900 as of the time of this post. Notable usages include a published book title, a more modern published article, and a quoteworthy quote. Can't find it in any dictionaries myself (besides urbandictionary!), but that doesn't mean a native speaker like me would see any reason to object. (In fact, I wouldn't!)

P.S. I should add that I can't compare the hits for "right doing" because they might appear in the middle of a larger sentence like, "I don't feel right doing my comparisons like that," in which case it's not just one noun; doing becomes a separate verb.