I think a "lefty" can be distinguished from a "liberal" (in the American context) by their treatment of power. To distinguish "left" from right-wing abuses of power, I'd have to have two parts of the definition:
A. A commitment to causes we usually identify as left-wing (shit, a tautology), and
B. A willingness to use institutional or state power in an "ends justify the means" way, especially if the underlying principle ends up being "it's OK when we do it."
A lot of people self-identify with the Left, but I don't consider people members of the real Left (the faction I'm concerned about) unless they're willing to coerce/manipulate/damage people and property in the names of the left-wing causes, and in a way that's instrumental, that sees people not as individuals but as means to an end. I'd add a willingness to use power in a way that doesn't respect property rights.
Caveat: Both A and B are necessary. If, at some point, someone merely uses left-wing causes as a power grab, we're dealing with plain-old megalomania wrapped up in social-justice talk. This creates all sorts of ambiguities.
Personal lifestyle choices and beliefs don't add up to Leftism. These choices may be liberal, in the sense that they don't coincide with the status quo or challenge the status quo in some way, but without the power element, they are just that, personal choices.
In every case I can think of right now, if you are applying the same sets of rules to everyone, you avoid the kind of Leftism I'm discussing. Leftist abuses of power virtually always involve using state or institutional power to pick winners and losers in a way that favors some groups and hurts others.