To have an overly simple example: A train station that slightly run down.

Reactionary: Not really into the whole train thing, thinks things would be better off if we didn't have them, and we just walked around more

Conservative: The train station is fine, maybe it needs a paint job or something.

Liberal: We should do a major renovation of the train station to bring it up to current needs, or maybe even to anticipate future needs.

Radical: We absolutely need a new train station, and if we don't get one, I'll burn it down so we HAVE to get a new one.

Man, and here I was figuring this would actually prompt a real discussion.

I am trying to add real content here, folks. :P

I'm a self-identified Conservative and Republican, and I'm fully in the "if it ain't broke, don't fix it" camp. Of course, some things are (in my opinion) broke, and do need fixing, and in some cases those are things the left have "fixed" and they do need to be brought back to what they were. So kind of a middle ground between these definitions of "reactionary" and "liberal," but not quite "conservative." Of course, I do see quite a few that seek to enact "fundamental" change, though perhaps not through "revolution" as this definition for "radical" requires.

Is this what you're looking for?

And following your train station analogy, I see it more this way:

Reactionary: "You know, the way they used to run the trains was a whole lot better. They don't do anything right anymore. And I don't trust these newfangled trains... I wish they'd use those steam-powered ones."
Conservative: "That track over there needs some repair, but overall it still works. Tear up those tracks, replace them, maybe touch up the place a bit, and it'll be fine.
Liberal: "There are problems here. Major problems. We need to redo whole track layout. Tear up all the tracks and re-lay every bit of it. And remodel the interior to redefine pedestrian traffic as well. Because none of it works."
Radical: About what you said. "BURN! BURN IT DOWN AND START OVER!"

@JK, yeah, that's a nice simplification.

There are major issues, in two areas, social and economic. Basically government control over people (social) and government control over companies (economic).

liberal (small l) literally means freedom, so seen in the context of government control, it can mean no control over people, and no control over companies -

Libertarian / Neo-Liberal is about freedom for companies to do whatever they please: reduce safety regulations and let the market manage these things, make it as easy as possible for a business to turn a profit.

Liberal is about personal freedom: Abortions for your own body, freedom from social profiling, freedom from exploitation by companies.

conservative (small c) means to keep what you have, that could be applied to the environmental movement (who may want to go back and undo the damage of industrialisation, like your Reactionary)

On the economic scale, you've got Neo-liberals / Free marketeers on the right (who think that a market free from any regulation and taxation can prosper and give people the most choice) and Socialists on the left (who think that the market should serve the public good directly, and redistribution of wealth is the best way to achieve social justice)

On a personal scale, you've got Anarchists on the anti-state side, who believe that any state action limits personal freedom, and Fascists on the state-ist side, who believe that state control is best for all.

(with Communism being a mix of heavily Authoritarian Fascist thought, and heavily Socialist economic controls)

You can be 'Conservative'* on economic issue, while being 'Radical'* on social issues. (ie keep the economy working as it is, but overturn the social norms that are holding us back from freedom - like gay marriage)

Or any other combination you like to choose...

I think in many ways the Democrats are reactionary. They are the ones constantly defending policies and programs that were designed in the 1930s or 1960s. They are the ones whose answer to every issue is a big centralized bureaucracy, a la the middle of the 20th Century. They are the ones whose most likely candidate for President in 2016 will be nearly 70 years old.

Who is the most likely candidate for President in 2016 of the Democrats then?

Hillary.

@dipplayer: Democrats may be Reactionary on economic issues - while being Liberal/Radical on social ones... (i don't know, and it probably depends on the democrat in question - it's not like they are one big homogenous party)

I also suspect that you've got a huge amount of populism (Democrat or Republican) - where the local politicians stand for the things they think will get them elected, rather than any actual position of their own. (you know, based on focus groups, and techniques borrowed from the advertising industry)

Because they are living in the glory days of the past, in this case the 1990s.