I'd be curious how you define podcasts and radio shows if you don't consider the distribution method. I don't see much light between the two other than the fact that a podcast show list is distributed via RSS.

Similar to why radio relates to electromagnetical transmissions in the radio spectrum. When it happens over internet, we don't call it radio, but possibly internet radio. RSS was the origin of podcasts, and if it does not involve RSS, it is not podcasts

Because the original idea of what we call "podcasting" is rooted on RSS.

The idea of what we call “writing” is rooted in stone tablets and chisels, but we still call Shakespeare a writer

There has been a significant longer amount of time between ancient civilizations and Shakespeare compared to today and l the first people who are recording audio content periodically and distributing it via RSS.

It goes much further than that: as the name suggests, it's coupled to a specific, obsolete brand of device.