they are all independent, but also can work together.
you can play Apple Music directly on the HomePod or airplay music from your phone
currently support for other services like Spotify is coming, although you can currently airplay Spotify from the phone though.
you can play the same music in all rooms, or different in each room (possibly limited by the number of streams you service allows)
you can pair 2 together for a stereo pair, but they must match, 2 mini or 2 full size, not one of each
a stereo pair should be in the same room.
You can also use a single speaker in a room.
then each speaker or stereo pair will be assigned to a room
you then select "living room + kitchen" to play music, or whatever combo you want.
I suggest a quick look at sonos, the price is similar,
you might have better luck with availability, and they're at more stores.
Ikea sells a sonos speaker for for $99
Sonos' basic speaker (the One) is $179/199 depending on if you want voice or not (you can pick Alexa or google, or turn it off)
sometimes you can save a few bucks if you buy multiple at once.
the ikea speaker is fine for background music, my friend has one in the bathroom, or if you just want light music while you work. If you plan on turning it up a bit and want some "thump", I'd probably go fer the Ones
sonos plays music directly on the speaker, which is a bit more reliable than airplay.
you can also make stereo pairs and assign to rooms and then group rooms like you can with HomePod.
Sonos can be controlled from iOS, android, Mac or windows, and everyone has access.
HomePods are a bit more limited, you can control easily from iOS, and sometimes Mac depending on how you're playing the music.
Sonos is better with TV and home theater, they have a couple sound bars, both have direct HDMI connection, which is more reliable than wireless. Also once you have TV audio in the sonos system, you can play on any speakers you want.
HomePod will allow you to airplay from an appleTV, but audio from apps on the TV or a cable box will not be available.
Sonos will allow you to add a pair of speakers as surrounds to a sound bar at the TV, HomePod is currently limited to only 2 speakers as a stereo pair in the front.
Sonos can access many streaming services including Apple Music. (Spotify, pandora, google music, tidal, and many more). And they also support airplay if you want it.
With sonos you loose access to siri, and homkit
the mini's have a new type of radio that will be probably be useful for home automation, it's called "Thread", currently there aren't many devices that support it, just a bulb and a LED strip from Nanoleaf in addition to the mini. Thread is really new, but might be more useful in the future. Although there aren't enough devices yet to justify it, Plus as other devices become available, you'll be able to get the same feature in other devices.