"Give me liberty or give me freedom!"
The left fights for "freedom" but the right defends "liberty."
What is the difference between freedom and liberty? As far as I can tell, they are pretty much synonymous. I have no hard data to back this up, but I suspect that the left uses "freedom" more and the right uses "liberty" more.
The operative difference isn't in what is being sought. It is in the verb which proceeds the noun. The left "fights for" it's goal: the implication being that we have yet to reach the desired end and need change to get it. The right "defends" the goal: the implication being that the status quo is good, but that it is being undermined and can be lost.
Radicals vs. fundamentalists. The word "radical" means "of or pertaining to roots." "Fundamentalism" means getting back to "fundamentals." So both radicals and fundamentalists want to get back to "roots" or "fundamentals"-two words which are, again, substantially synonymous.
Words do shift meanings. There are 19th century Papal bulls which denounce a number of liberalizing ideas, viewed as anti-clerical. One bull, startlingly, denounces "progress." Something may have been lost in the translation from Latin, but it is pretty clear that "progress" in the original sense, is different from "progress" as we use it today. Then, it meant a specific political trend which was antagonistic to the church. But today, everyone, regardless of religious or political stance, favors "progress."
Civil liberties vs gun control: these causes are also framed as being on the left/right continuum, but are really two sides of the same coin. Both of these assume American Exceptionalism, and are seen as being fundamental rights. Both are essentially declarations that the individual matters more than the government and that individual rights "trump" government prerogatives.