You got a few things wrong here.There are two things that Apple Music represents, let's look at each one individually so you understand:
1. "Radio" In iTMS, it's called "iTunes Radio". In an app, it's called Pandora. In Apple Music it's called "For You", "Playlists", and "New". There is nothing that Apple Music can do in these various versions of "Radio" that iTunes Radio and Pandora can't do for free.
2. "Library" In iTMS, it's called "paid downloads". In Apple Music it's called "offline". iTMS it costs $1 per song. Apple Music it costs $120 a year. Both do the same thing, both cost money, just one is a hell of a lot more money.
So, when I say that iTunes and Apple Music are the same thing just marketed differently and all the 'great' features of Apple Music are currently available for free that's what I'm talking about. "For You", "Playlists", and "New" is just marketing nonsense that translates to "iTunes Radio Custom Stations" which cost nothing. "Offline" is just marketing nonsense that translates to "sucker, you just paid $120 a year for the rest of your life for Feel My Face ha ha".
BJ
The Radio feature is listed as "Radio" in both iTunes and Music.app with Apple Music enabled. Beats 1, featured stations and user-created stations are completely free; without a subscription. They basically just got rid of the branding "iTunes Radio" and added Beats 1.
For You is totally different from Radio. For You takes into account songs/albums you've listened to and ones you've "loved" and gives you curated playlists from music professionals and publications. There are playlists made for "best of" lists, current references (e.g. ghost writing discussion in hip hop), moods, activities, etc. Radio is created based on a single song, artist, album or genre and tweaked with playback but each radio is a separate entity.
Yeah, they're both serving you listening recommendations but I don't think that's enough to say they're the same.
New is just new music and top charts. It basically serves as iTunes Store-like front for Apple Music. The name isn't apt but it's not pretending to be a curation or recommendation generator. Playlists is just your playlists lmao...
On streaming vs. purchased, value is subjective. If you listen to enough music yearly that you would have to pay more than $120 a year to buy, it may make more sense for you to stream. Especially, if you get on a family plan. And some people actually like the curation stuff, I am one of them. It's nice to let go of having to have complete control over everything about my library and what I listen to next.
Offline is just that. Having your music available in the absence of wifi can be very useful.