Apple TV is a physical product that is often referred to as a set-top box. Apple TV comes with a remote control, and it can be used with almost any TV that has an HDMI connection. Even the most basic of TVs will be able to connect to Apple TV with the use of an HDMI as long as that particular model is compatible with that specific TV. For example, Apple TV 4K is not compatible with TVs that are not 4K, and it cannot convert your smart TV into a 4K TV, or course.
Basically, the Apple TV set-top box allows its users to connect to the internet and stream content on a TV that is otherwise not a smart TV, allowing them to stream and even use screen mirroring.
Users 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 using an Apple TV set-top box.
Apple TV+ is a streaming service, not a physical device like the Apple TV set-top box.
Users can watch exclusive movies, TV series (like the aforementioned Ted Lasso), including but not limited to Apple Original shows and movies. Users don't need a specific app to use Apple TV+, but they can access it on any Apple product (iPhone, iPad, Apple TV, Mac, etc.) or 3rd-party devices like Roku and Smart TVs.
Apple TV+ does require a monthly subscription ($4.99 a month), though there are often year-long free trials for Apple lovers who buy a new Apple product. This common promotion is offered because Apple TV is in its early years still, not having been around as long as its predecessors Netflix and Hulu.
The Apple TV app allows users to access the same benefits and features as the Apple TV set-top box. The Apple TV app comes standard on all Apple devices, allowing Apple users to easily use it's many features right on their iPhone or iPad.
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 the app. You can access all your Apple TV+ shows (if you have a subscription or free trial) as well as anything else you could normally watch on an Apple TV set-top box.