A Democrat is a person who is a part of the Democrat party. It is more precise to say someone is "left" when you argue about economics because regardless of their political affiliations their economic persuasions are the same. It is like saying X is a midfielder, as opposed to saying X is a goal scorer. Anybody can be a goal scorer but only midfielders are midfielders.
The liberalism discussed on these boards generally refer to the American meaning. Even there, the classic liberal was basically what a Libertarian is. That's not the case anymore (basically the opposite). There are, like any ideology really, different strands here and there in libertarianism but they're probably more alike/differ less than other sects of other political ideologies.
In Australia the smaller parties generally are left when it comes to economics, except for the National party. I am in a dilemma though since I don't think either the big parties are good and it is mandatory to vote in Australia
. I generally vote Greens or National party.