A problem is something wrong with the world. A challenge is something addressed to you. The facts do not move when you swap them, but your position does — one puts you underneath the thing, the other puts you across a table from it.
Watch what the body does with the swap. Shoulders drop half an inch. The situation stops being weather and starts being work.
That difference is not decorative. A great deal of what makes a hard month unbearable is the sense of being rained on rather than engaged, and rain is the one thing nobody has ever been able to answer.