Apple TV 4K
There are now 4 models 4K. Which one do you have? Identify your Apple TV model - Apple Support
All of a sudden I have iTunes Store
The iTunes Store on Apple TV is for buying or renting movies, or buying TV shows*. If that is something you want, then you can buy in the TV app, the Movies app, or the TV Shows app*.
Technically, all digital products and services with payment through Apple are handled by this same division of Apple.
Currently, you can’t buy music, music videos, books, or audiobooks on Apple TV.
You can subscribe to Apple Music if you want, as an alternative to Spotify/YouTube Music/Amazon Music.
[* TV Shows are available for sale from the iTunes Store in select (6) countries.]
I have to listen to Apple Music
Not necessarily. You can also listen to Home Sharing music (Computers app), Spotify, internet radio, YouTube, Amazon Music, Tidal, etc. Find apps in the Apple TV App Store - Apple Support.
The Music app on Apple TV is for online streaming music content from Apple’s servers; subscription or purchases.
and I don't know what Arcade is.
Apple Arcade is gaming – subscription style, with curated game apps for the Apple Arcade platforms (Mac, iPhone, iPad, Apple TV box). [Done with game 1? Then pick a different one.]
That's all it has.
Thousands more apps in the on-device App Store. Find apps in the Apple TV App Store - Apple Support.
And it confuses the rest of my devices.
How so?
The box says that it can be used as a home hub but I struggle to see how. Or am I misunderstanding the concept of Home Hub?
The home hub device is the device that links home automation devices together to your Apple ID account and to iCloud, through an always-powered device in your home. It is mostly passive that way.
The home hub is not a management device. You manage HomeKit in the Home app on iPhone or iPad.
About the Home app - Apple
Set up your HomePod, HomePod mini, Apple TV, or iPad as a home hub - Apple Support