Some will have been re-processed to improve sound quality. Modern software and hardware can work minor miracles. Others may not have been processed if the originals were of good enough quality.
Bear in mind that the original studio recordings may have been better quality than the broadcast medium of the time, so if you heard something on analogue radio (or on cassette or vinyl), you may remember them as poorer quality than they actually were recorded originally. Even in my time in broadcasting, analogue tape could store almost the full range of frequencies a human could hear, and listening to the original tapes on good quality speakers was clearly much better quality than hearing the same thing broadcast.
Older master audio tapes which might have deteriorated over time can sometimes be "oven baked" to make it safe to play them and bring them back to life for a while, especially if the tapes were kept in non-ideal conditions, e.g. a valuable old tape salvaged from someone's attic. Although often this temporary fix will lead to quick degradation after a while, it makes them sufficiently improved to be copied and processed in the short term before any new degradation sets in. Once digitised, there is less need to keep the original tapes. Or if you do keep them, less worry if they "die" before you next use them. I forget now how this "baking" works, but plenty of info out there on the interweb if you search.
This is of course a particular worry for libraries, archives and museums which keep old recordings - the tapes degrade over time, no matter what the original quality was. Broadcasters and archives try to keep old recordings under conditions as ideal as possible to try to extend the life of tapes. An interesting quirk is that reel-to-reel tapes may be stored wound back to front for less risk of magnetic print-through causing pre-echo.
Modern audio processing software and hardware can make a real and genuine difference to the quality of old audio tapes. And of course, since the lifetime of analogue tapes is finite as the tape itself degrades, everything has to be digitised to preserve it.
I have an extensive collection of old Welsh music recordings (cassette, vinyl and 78rpm's) and I try to digitise them as I get a chance while the media and my playback machines still work. I use Audacity software for the most part to do this, and it's remarkable how much you can achieve with fairly straightforward software like Audacity. Such as removing clicks from records and tape hiss and noise reduction (sample a piece of background noise, then use the software to follow and cancel out the noise). If I can achieve this sort of thing with fairly simple free software at home, imagine what professionals can achieve with modern software and hardware.
As a local Welsh language recording company (Sain) found in recent years, when they bowed to pressure to digitally re-release older Welsh recordings (a little streaming income from old material is better than none), the old multitrack audio tapes from the 1970s and earlier were usable after a bit of "baking". The
real problem was that they no longer had the old analogue machines to play them
and had to send the tapes away to be digitised to specialist retrieval companies which keep old multitrack and reel-to-reel machines going for this very purpose.
Bearing in mind it's over 20 years since I was a sound technician (unsound technician?), technology's moved on quite a bit and I'm sure AI will bring further advancements in the audio field.
