Both use home wifi for connectivity, support Siri, and generally will act independently once they are set up from the rest of your devices.
Both support the thread mesh protocol and will bridge thread (which is IPv6-based) to your local network so you can IoT it up.
Both act as Matter controllers, a new home automation standard which uses wifi and thread.
Both apparently have humidity and temperature sensors? Who knew!
The SoC is from the Apple Watch, and the HomePod has a newer generation by virtue of being released later.
There are more differences compared to the original HomePod, because it didn't have the same sensors or networking hardware and had a higher BoM/retail price.
Notably, the wifi is actually 802.11n now rather than 802.11ac - probably because the didn't feel the need to have a watch support 802.11ac.
Two HomePod mini set up as a stereo pair likely sound better than a single HomePod, and run at 2/3 the cost. That said, I have some large spaces I'd love to try a stereo pair of these new models in.
If you want whole home audio, you can just buy the minis. They just operate via Wifi.