While handling the issue specifically refers to focus on a technical problem the client is trying to solve, coaching the person is about helping the coachee learn about the situation and themselves to develop the behavioral change that will help them deal with the problem.
This is one of the traps I fell for with one of my coachees.
First, why do I call it a trap? The trap comes when a coach gets stuck on helping the client find solutions to the problem rather than focusing on the client’s thinking behind the solutions.
When trying to help a coachee both handling the issue and coaching the person are plausible paths to take. However, the former is more an approach a business leader would take; it focuses on a transactional goal trying to find solutions. The latter is more aligned with the coaching approach since it involves a transformational goal that leads to a behavioral change.
It doesn’t matter what solutions the clients pick but how they reason that decision.
If you are interested in giving more thoughts to this topic, see the book “Co-Active Coaching” (Kimsey-House, et al. 2018), page 47 under the tittle “The Coach is Listening.”