What is a story theme? Is it any different from a story problem?

from Beginning Writer's Answer Book, edited by Jane Friedman

Writers disagree on the exact definitions, but here’s one explanation: A theme is the message an author imparts to his readers through the plot and characters in his story. The writer starts with an idea, and as his story develops, it is influenced by his own philosophy or observation of the human condition. This is his theme. A story problem is the vehicle by which an author presents his theme. For instance, the problem facing Dorothy in The Wizard of Oz is getting home to Kansas. Through her trials and adventures in the Land of Oz, she realizes her folly in wanting to run away from home in the first place, and finally decides “there’s no place like home,” which is the overall theme of the story.