The CDs that carry compression to the extreme use a technology in which the sound is processed in multiple frequency bands simultaneously, so that the signal is divided up and the average level is raised and kept high within each band before the signals are are summed back together again.
When you hear a recording like that over the radio, you're also hearing the processing that the radio station is applying--and radio stations do a large amount of applying. People tuning across the band (especially in their cars) stop on the stations that seem "strongest." In the battle for market share, ratings and advertiser dollars, the "loudest" sounding station often wins. Someone here posted a link to one of Bob Orban's papers--his various compressors were the standard weaponry for decades, and I think that he is none too comfortable with a lot of how they've been used.
But often it's more than just loudness--stations that are heavily into competition with other stations in their same market go for a distinctive "house sound," and if someone played you the same track recorded off the air from one radio station versus another, you could soon learn to tell which station had broadcast it, and as a faithful listener to one of these stations, nothing you would hear on another station would sound quite right to you.
(That says something, or it should, about the perceptual traps of "shootouts"--there are many ways and many reasons for human beings to become attached to things being a certain way, especially when we have no way to know the truth of a situation, and we are left to choose among various representations of an unknown set of circumstances. Come to think of it, rumors and Internet scams and conspiracy theories work that way, too.)
--best regards