Liberal, progressive, advanced, radical are comparable when used of a person or thing (as an idea, a writing, or an organization) to denote being freed from or opposed to what is orthodox, established, or conservative.
Liberal implies emancipation from what binds the mind or will and connotes either indifference to tradition, convention, dogmas, or laws or the rejection of one or more of these. It therefore may suggest tolerance and broad-mindedness on the one hand, or unorthodoxy, laxness, or even lawlessness, on the other.
Progressive is commonly a relative term, because it usually implies a comparison with what is reactionary or backward and a willingness to forsake old and seek out fresh methods and beliefs in the search for betterment. The term seldom suggests the espousal of extreme policies.
Advanced is usually applied to men or to ideas and discoveries that are, or are believed to be, ahead of their time. It can favorably suggest liberalism or progressiveness and distinctively connote mental daring or it can unfavorably suggest an extreme of foolhardiness and experimental impracticality.
Radical often is employed in place of advanced, but discriminatively it may imply a willingness to root up and destroy the institutions which conserve or propagate the ideas or policies condemned; it is often therefore virtually interchangeable with revolutionary. All of these words are capable of being used disparagingly especially as applied to politically active individuals or their works, often with little thought of their meaning content in more general applications.