In my experience, over 90% of students who think they are great at understanding math but bad at doing exercises don't really understand the math, they have severe conceptual errors as well as bad approaches to solving problems. Similarly, the overwhelming majority of mathematics students who say they have great intuition but are bad at proving things don't actually have great intuition, they just find talking about connections and speculating about analogies fun, but don't like the part where people read what they write and say that their argument has gigantic gaps or is complete nonsense or is an attempt to prove something false.

Of course, there are some mathematicians who are better or worse at recalling or finding and proving key lemmas. Some mathematicians are better or worse at writing things up in a clear and interesting fashion. There are mathematicians who have done great research after mediocre results in coursework, and vice versa.