Thanks for the examples. I think I understand what you are asking now.
I have often read articles describing graduate education talk of "unstructured research problems". What exactly does an "unstructured research problem" mean?
In much of one's undergraduate work, one is assigned problems where the person doing the assigning has at least one solution, and solution method, in mind. The assigner has structured your work for you. Also, the assigner has given you a due date!
But the thesis is the thing that will prepare you to be an independent researcher, finding problems of interest to others, solving them, and presenting the solution in a compelling way.
Although there are exceptions to this, for a PhD, no one is going to hand you your assignment and say, solve this, and hand it in to me in three months. Your advisor might say, read this paper, tell me what you think; then you might say, the authors suggested applying their technique to such-and-so other problems, and I'm curious to see if that would give useful results; and the advisor says, a collaborator of mine actually tried that once, and didn't get anywhere, but I've been thinking about the experimental set-up he used, could you take a look at it and see if you can come up with a way to.... And then you're off and running. Only you don't know whether the improvements that you spend three months designing and building are actually going to get you anywhere.