Q: Does apple tv 4 th gen stream everything in full hd or 780? Do tv channels get streamed in full hd?

It will streams HD if it's HD or 720p if it's 720p.

There a setting for HD or 720p.

It streams in whatever you select in settings. It can do 720 or 1080p.

Get help playing or streaming content on your Apple TV - Apple Support

Standard Definition is 720

High Definiton is 1080

Just to add onto the other posters comments, the various apps could vary or compress the content provided. For example, Netflix throttles the compression based upon the users ISP speed. Whereas iTunes videos will maintain the true 1080 as it will download a copy of the title rather than a traditional "stream"...

You're welcome.