HD radio stations require a radio capable of tuning them in. It is free once you have the compatible tuner. Most large radio stations have HD sub-stations and the genre can vary as to what those sub-stations play. It basically expands the channel/station numbers. I have never been successful at picking up HD stations any great distances from broadcasting towers even though I can often get the parent station fine. So it's more an in and around town thing. Guess they broadcast them at different frequencies or lower power or something. But it can be a cool feature to have if replacing a tuner in a vehicle, and usually doesn't cost any extra to get an HD compatible tuner.
The digital piggyback degrades with range where the tuner can no longer process the digital signal without it affecting quality and creating fragments. Analog signals just degrade in quality and signal level over distance. But you can still often receive analog. These are very broad non-technical generalizations in my post and then you have AM and FM which are really quite different. The whole subject would baffle millennials.