A right libertarian believes that the best government is the smallest and most local, and that the government cannot and should not regulate sex, drugs, guns, or businesses.

A left libertarian believes that the best government is one that regulates the economy, protects the public commons, and safeguards the rights of minority groups but otherwise leaves people alone to do as they will.

I'm much more familiar with the former, so if I've erred in describing the latter someone please correct me.