In basic research, such as pure mathematics, one might naively expect that the natural question to ask with regards to a given problem X in a field is

"What is the answer to X?".

But in many cases the more valuable question is

"What can be learned from studying X?"

The answer to X itself can of course be one of the things learned in this process of study; but one can learn far more useful information besides, such as

What are the main difficulties to overcome to resolve X?

What new techniques can one discover in order to solve X?

Why are existing techniques insufficient to solve the problem by itself?

How does X relate to results in prior literature?

Can one uncover new connections between X and other topics Y, Z, ...?

What are some natural related or followup questions X', X'', ... to study?

Nevertheless, until recently the two questions were closely aligned, to the point where it was not really necessary to distinguish the two: the only practical route to solving a difficult problem was to first address many of the subquestions listed above. (1/3)