In the late 19th century there would often be violent physical confrontations between the communists and the socialists and those who opposed them, right on the floor of the French House of Parliament. As a result, the french segregated the communists and the socialists to the left side of the center isle (the left wing) of the French House of Parliament. The terms Left Winger or Leftist have been applied to those who favor communist or socialist ideas ever since.
The term "Right Winger" is much more vague and simply refers to anyone who strongly disagrees with communisim and socialism and or communist/socialist principles. The more strongly anti-communist/socialist a person is the farther right they are.
Example:
I think Communisim and Socialism are among the most authoritarian and totalitarian systems of government ever devised and I strongly oppose them. Thus I am a "Right Winger".