When Mr. Bush’s brother George first ran for president, he erroneously referred to Greeks as “Grecians,” flubbed the name of India’s president and confused Slovenia with Slovakia, offering the world an unabashed portrait of provinciality.

But across Europe this week, Jeb Bush revealed himself to be a very different kind of Bush: well traveled, almost encyclopedically knowledgeable about foreign countries, and possessing the genuine inquisitiveness that his brother had so notably lacked.

In many ways, the impressions are superficial. Mr. Bush is now six months into a seemingly perpetual noncandidacy that has allowed him to forestall the kind of detailed plans that might disappoint allies, domestic or foreign. In Europe this week, he refused to offer specific answers to some of the most urgent problems facing the countries he visited, repeatedly saying that he was not yet a candidate.

Yet Mr. Bush has benefited from comparisons to the foreign travels of Republican rivals like Gov. Scott Walker of Wisconsin, who breezed through Israel without public events or tough questions. Mr. Bush crafted his tour here around his fluency in foreign affairs, holding news conferences in every country he visited.