How did "changing horses at an inn" work in Regency-era England?

I have recently been decompressing from the stresses of the world by reading various pleasant romance novels set in Regency-era England. Something that has come up more than once is that, if the characters have to leave London for some reason, they'll either hire a vehicle and some horses and trade out for fresh horses at inns along the way, or start out with their own horses, change horses at an inn, and have their own sent back home while they travel onward. While I assume that a lot of this is just the authors needing to get the characters from Point A to Point B without spending a lot of pages on horse logistics, I also would assume that there's some kind of historical reality behind this idea somewhere, even if it didn't really work at all like how they portray it. I figured I would ask here because I have a lot of subsidiary questions about the whole concept.

Was this indeed a thing? If so, how widespread was it and how did it actually work? Would most inns have horses available, or only ones in high-traffic towns? How many horses would they have in rotation? Did you have to leave some kind of deposit, and did they expect to get their horses back on your return trip? Could anybody do this, or only men who seemed reasonably solvent and trustworthy? If there was a big quality differential between the horses you started with and the horses you wanted, would you have to pay cash in addition to the trade? What if you were making a one way trip, would you just sell off the horses at your final destination and call it a day?

I would close this by saying "I don't know anything about horses," but I'm sure that's already evident. Thank you for any insights you can provide.