At its core, the difference between problem-solving and decision-making is that problem-solving is an additive process, while decision-making is a reductive process.

Problem-solving is about finding more solution(s) than what is currently available. This can be finding one solution from not having any at all, or finding potentially better solutions from the existing ones.

Decision-making is about filtering out already found solutions down to one, or several solutions for multiple contingencies.

They obviously can be used together to achieve a goal. First, you add more solutions using problem-solving and then you reduce those solutions using decision-making.

Once you found the best solution(s), then it’s execution/implementing time.