MOSCOW—In Syria, Russian President Vladimir Putin is trying to take a page from his Ukraine playbook by keeping the West guessing about his plans, employing the military art of deception known in Russia as maskirovka, or camouflage.

Last year he surreptitiously sent Russia’s army into Ukraine, reversing the advance of Ukrainian government forces and bringing pro-Russia rebels a more-favorable peace settlement. Now, he’s repeating the gambit in Syria: shoring up his ally, Syrian President Bashar al-Assad, and ensuring the...