The confusion seems to be the result of the fact that "liberal" has different meanings in America and Europe. In the US "liberal" means someone on the left who believes in a combination of social liberalism, public welfare and a mixed economy. The American right wing has been relatively successful in giving the word "liberal" a negative connotation since the 1980's, hence the rise of the word "progressive".
But in Europe "liberal" is associated with classical liberalism, which is someone committed to the ideal of limited government, individual liberty and free markets. The difference has to do with the fact that the term, which originated in 19th century England, was never adopted in the US until the 1930's when FDR coined it to describe his New Deal policies. European liberals can be thought of more as "Libertarians" in the American context. Think Bill Maher.