You have prompted me to prepare a "roadmap" for my own sanity...
Apple Device Interaction
By Michael Paine, August 2020
Mac computer
MacOS (Mojave)
iTunes app
Airplay >> Video/audio output to Apple TV, Homepod etc
Homesharing >> Media server for Apple TV
Air Video HD app* >> server for audio/video on iOS & Apple TV
HD Homerun app >> play free-to-air TV being streamed from HD Homerun server on local network #
iPhone / iPad
iOS/iPadOS
Music/Apple TV app
Airplay >> Video/audio output to Apple TV, Homepod etc
Remote app >> control music on a Mac (incl Airplay)
Air Video HD app >> play audio/video from a Mac running AIr Video
HD Homerun app >> play free-to-air TV being streamed from HD Homerun server on local network
Apple TV
tvOS
Settings app
Video and Audio
Audio output >> select Homepods etc@
Music app >> select & play Apple Music (mostly subscription)
Computers app >> stream music/video/photos from a Mac running
Homesharing
Air Video HD app >> play audio/video from a Mac running AIr Video
Channels app >> play free-to-air TV being streamed from HD Homerun server on local network
Notes
Generally all devices using Airplay can override an existing Aiirplay connection. Sometimes the user gets a warning that another device will be disconnected.
Not all Apple TV apps can output to Airplay (eg Homepods). Also lip-sync may be out for some apps.
* There are several apps like Air Video HD that act as media servers, including Plex. These apps are unable to play protected video purchased/rented from the iTunes Store.
# HD Homerun is a TV tuner that is connected to a local network and allows Macs, iOS devices and Apple TV to play free-to-air TV
@ Some Apple TV apps also allow audio output selection by swiping down to reveal a settings menu