"There are some people who want to split things into "yuri" and "rezu" based on whether those have sexual content, but this distinction doesn't exist."
So it is like the distinction between "shoujo ai" and "yuri".
Ah, no, not quite. In Japan, there is some discussion about the exact meanings of "yuri" and "rezu" (and "GL" as well) but as for "shoujo ai" everyone knows what it means. "Shoujo ai" means heterosexual loli porn.
Here, in the English-speaking world, "shoujo ai" was at one point fanspeak for soft yuri, but it's become obsolete since then -- mainly because people found what the real meaning of the term in Japan was!
That being said, I actually have a harder time understanding compensated dating than I do outright prostitution. Paying for sex is pretty straigh-forward, but paying for someone to essentially just hang out with you for an hour or two kind of baffles me. Sure, she laughs at your jokes, listens to your problems, compliments you, but like, of course she does, you are paying her for it.
For whatever reason, Japanese culture seems far more comfortable with that sort of fake companionship. It isn't even a new phenomenon, since that's basically how the geisha system worked (and works).
It's how the whole hostess club system works as well. To quote:
"Hostesses light cigarettes, provide beverages for men, offer flirtatious conversation, and sing karaoke to entertain customers. Hostesses can be seen as the modern counterpart of geishas, providing entertainment to groups of salarymen after work. Hostess clubs are distinguished from strip clubs in that there is no dancing, prostitution, or nudity."
Strange that some commenters claim they don't understand the point of such an establishment. It appears they share the old chauvinistic notion that women's only use is sex. It has never been the way the Japanese think, though: in their culture, all interactions with women have value -- and it makes perfect sense to pay to have women talk with you, sing, play music for you, etc.