The effect you describe is called tape compression. Many people do tend to prefer that tape effect over digital...that's why many producers and engineers still prefer to work reel to reel recorders rather than digital, and many more use some combination of the two.
As far as the FM goes...the signal could be compressed, it could be the CD player or turntable they used, etc.
As far as the FM goes...the signal could be compressed, it could be the CD player or turntable they used, etc.