Russia launched airstrikes in Syria on Wednesday, catching U.S. and Western officials off guard and drawing new condemnation as evidence suggested Moscow wasn’t targeting extremist group Islamic State, but rather other opponents of Bashar al-Assad’s regime.

The arrival of Russian warplanes and helicopter gunships catapulted the Syrian crisis to a new level of danger and uncertainty. Moscow’s entry means the world’s most powerful militaries—including the U.S., Britain and France—now are flying uncoordinated combat missions,...