the aTV-HD and aTV-4k both have the app store.
They aTVs do have with a few default apps, which you can't delete, but they're all apple or system related (no third party), like search, settings, photos, and the various app and media stores. You can "hide" them in a folder if you don't want them taking up space on your main screen.
Even "basic" apps like Netflix or Amazon Prime have to be installed by the user.
if you go to the App Store on your phone, apps should have an "also offers aTV app" version of their screen shots (at least the entry for the Netflix app does, not sure if all compatible apps do this)
it doesn't appear there's a way to browse the store on the web.
--edit
I found the online App Store, but it's not broken down by device. So you have to open an app, and then see if it has an tvOS version.
here's the main store, where you can search for things
Find and download top apps and games for iPhone on the App Store.
apps.apple.com
and here's the Netflix page as an example
Download Netflix by Netflix, Inc. on the App Store. See screenshots, ratings and reviews, user tips, and more games like Netflix.
apps.apple.com