Apple TV is a physical box with a remote control, and it can be used with any TV that has an HDMI connection. Even the most basic of TVs will be converted into a smart TV with the addition of an Apple TV. The Apple TV box is much more than just a streaming service, but rather a full media player.
You can access Netflix, Disney+, Amazon Prime Video, and HBO Max on your Apple TV device, as well as Apple Arcade, Apple Music, and Apple Fitness.
Apple TV+ is a streaming service, not a physical device. You can watch exclusive movies, TV series (like the aforementioned Ted Lasso), and other shows made by Apple. You don't need a specific app to use Apple TV+, but can access it on any Apple product (iPhone, iPad, Apple TV, Mac, etc.).
The Apple TV app is essentially the app version of the physical Apple TV and it comes standard on all Apple devices. There is also a long list of Apple TV app-compatible devices if you're curious about whether you already have a device that works with with the app. You can access all your Apple TV+ shows (if you have a subscription) as well as anything else you could normally watch on a physical Apple TV box.