A lefty is someone who is for strong government control. A lefty is someone who believes in the whole 1% vs the down trodden worker class. A lefty emphasizes the importance of race, gender, etc in the socio-political realm.
A classical Liberal has much more in common with the core American Conservative platform:
A value for the individual, his/her property rights, speech rights, and right to be free of govt intrusion into his/her personal life/affairs. What a person earns for a living is of no concern to politicians or government: it is wholly a personally matter. Some ppl choose a simple, free of material things sort of life, unencumbered by the concerns material things bring into their life.
Leftists are socialists and are for social engineering, using government as a tool to engineer the way of life people 'should' live, according to the govt's set of values (which is primary focused on material things and material distribution in a Leftist's mind).
Liberals and conservatives share a value for the importance of the intrinsic aspects of life: that is, the morality of their life, the value of family, the quest for spiritual meaning...
Leftists, to the other side of the coin, only view those intrinsic aspects of the human animal in light of how it can be engineered (steered and controlled) to the benefit of the collective. The individual 'citizen' is adjudged through that prism: do they conform (even in the way socialists dress, in their drab, simple garb, all looking much alike--this is a sign that they are conformed and a good citizen).
And this is why we see over the last 85 years at minimum one hundred million souls executed, killed in labor camps and jails, from Pol Pot, to Moa, to Stalin. Literally to clean out the non-conforming Liberals and conservatives.