I'm positive it is a different skill and I even think that those two skills can be at odds at times.
Poorly defined problems often come down to things like creativity and your ability to handle emotions. Sometimes you have to follow a seemingly senseless curiosity to find the right path forward. Sometimes it is about finding beauty where it isn't expected. Also these problems have multiple valid and fundamentally different solutions and can be highly subjective. Think art.
Well defined problems are about juggling multiple things in your head, high concentration, relying on fundamental knowledge, heuristics etc. All of that possibly under pressure. There might be multiple solutions but they are typically on a scale (good enough vs perfect etc.) or are choices between measurable tradeoffs. Think engineering.
