Part of the difficulty the average person encounters in trying to follow present day ideological debates is a confusion of labels. Lots of people don't like labels, of course, but the fact is they are extremely useful and very hard to avoid.
As an example of label confusion, consider that modern conservatives hold views which in the 19th century were considered liberal. Thus, conservatives today are sometimes referred to as classical liberals, which is certainly confusing.
On the other hand, modern liberals hold many views which in the 19th century were associated with socialism. Today these liberals/socialists are often referred to as progressives, which has a more innocuous ring to it, at least to the ear of many Americans.
This short video does a nice job of illustrating three basic differences between classical liberalism (i.e. modern conservatism) and modern progressivism. There are other differences besides these three, to be sure, but these are pretty fundamental: