Yes, they are both kinds of libertarianism[1], the main difference is that left wing reject private property (not personal property), which is argued that its existence will create power structures thus defeating the purpose of said libertarianism.
1: “One gratifying aspect of our rise to some prominence is that, for the first time in my memory, we, ‘our side,’ had captured a crucial word from the enemy . . . ‘Libertarians’ . . . had long been simply a polite word for left-wing anarchists, that is for anti-private property anarchists, either of the communist or syndicalist variety. But now we had taken it over..." - Murray Rothbard
1: “One gratifying aspect of our rise to some prominence is that, for the first time in my memory, we, ‘our side,’ had captured a crucial word from the enemy . . . ‘Libertarians’ . . . had long been simply a polite word for left-wing anarchists, that is for anti-private property anarchists, either of the communist or syndicalist variety. But now we had taken it over..." - Murray Rothbard