I'm not going to rehash what he's written - if you're interested in examples for his three categorizations, you can pop over to his site and have a look. What I did want t add, though, is something that has become one of my language education-related pet peeves.
Whenever I ask my students about their winter/summer/spring vacation or what they did over a long weekend, I inevitably get: "I played with my friend." This is where I try in vain to teach them to use the expression "hang out." "I hung out with my friend," I tell them. They rarely remember. But you can hardly blame them - the textbooks always translate 遊ぶ as "play." I'm sure there are people who will tell you that "hang out" is not proper English, but do you know of any teenagers or adults that get together to "play?" Whenever I have the opportunity, I try to explain that "play" is used mostly just for children in this context and "hang out" is for anyone who's not a child.
But alas, just as sure as the automatic Japanese reply to "How are you?" will always be "Fine, thank you. And you?" I don't see this play/hang out confusion getting better any time soon.