The former is traditional philanthropy, but the latter is an interactive way to support content creation. I'm not saying that those models will necessarily translate to Medium, but that certainly seems to be the idea.
I urge anyone that's curious to go give Twitch a quick look. Spend a good half hour in a few different channels. It's really interesting. Some of the streams are what you would expect: skilled gamers playing at a high level. But many of them are very creative in how the develop a community, how they interact with viewers and chat, and what sort of entertainment experience they provide. I think that most people will 'get it' if they watch for a bit. It's compelling entertainment, and lots of people are willing to throw a lot of money at it.
The point is that it's just an entirely different phenomenon from philanthropy. NPR and Wikipedia really have no place in this discussion because they are so different.