Apple TV do I have to buy the box or can we download app

As Jonamiller mentioned if your TV supports the Apple TV app you can do without the box. However I have found having the Apple TV 4K box a much better experience than using my TV's user interface. Please look in the following link to see if your TV is one of the TV's supported to get the Apple TV App.

https://www.apple.com/apple-tv-app/devices/

You also may be confusing the Apple TV App with the Apple TV + streaming service. It can be confusing if you are unfamiliar with Apple's TV products. You can view each of them (they are all different) by clicking apple.com/tv. You will find they include:

• Apple TV (App)
• Apple TV + (service)
• Apple TV HD (hardware)
• Apple TV 4K (hardware)
• Airplay
• Accessories

If your TV supports it, you can download the TV app for free. Alternatively, you can download it on your iPhone and stream to the TV if your TV supports AirPlay. For a more streamlined, easy experience, buy the Apple TV box.

The Apple TV set-top box offers much more than the Apple TV app. The Apple TV app is just one of the apps on the Apple TV box.

The Apple TV set-top box also offers Home Sharing, AirPlay, several Apple cloud services, a choice of thousands of third party apps, Dolby Atmos*, etc.