Leftie tends to be used to describe the far left usually with some kind of "political correctness gone mad" scare story angle, along the lines of the Baa Baa Black Sheep ban story or Jenny Lives With Eric and Martin.
The tabloids of the time (mid-eighties) would refer to alternative comedians as loony lefties, contrasted against traditional comedians like Benny Hill, Bernard Manning and Jim Davidson (still making jokes about race, sexual preference, religion, gender in a pejorative ..today's word.. way).
It's a tabloid shorthand for anything beyond the Western European socialist model (something that hasn't existed as a political choice in the UK since 1994).
Left-Wing is subjective as more Right-wing countries have a righter-left. The USA is in a general sense more Right-wing than Denmark (not that the Danes are without a fringe far Right movement of their own).
For example, the ideas of private gun-ownership and capital punishment are seen as a sort of a oddity to much of Western Europe (our Right-wings might have a fringe that are interested in restoring such things but even then they are generally seen as fruit-loops along the lines of the UKIP guy claiming gays cause storms).
In the USA these are topics of genuine controversy even within the Left-wing.