How do liberal and radical political philosophies differ?
The main difference is that the liberal political philosophy is inherently democratic and focused on the idea of individualism. Radical political philosophies like Marxism are much less like this.
To a liberal, one of the most important things is the liberty of the individual, both economic and social/political. An individual must be allowed to do and say things that might, overall, not be best for the society as a whole. They must be allowed, for example, to express racist ideas or to engage in practices that waste resources even though it would be better for us all if they did not.
Marxists, by contrast, are much more focused on what is perceived to be the good of the whole society. They have no problem with taking away the rights of the people to do certain things if those things would hurt society as a whole. For example, there is no problem, in Marxism, with suppressing the rights of people to criticize the government. This is because Marxists believe the government (as long as it is Marxist) knows what is best and has the duty and right to do whatever it thinks is necessary to help society as a whole.
Overall, then, liberalism is much more individualistic while radicalism tends to be more communitarian.