A confusing reply; meaning it is ALL software. The update of the app is software (the Alexa app used to display this, but it doesn't anymore.) When the Dot gets new software update the app displays it as "Device software version" and it is automatically updated when a new one is released. This is also known as a firmware (FW) update in the trade.
So, which comparable software in, or for, the Home are you referring to; the app or the FW? Just like with a Dot, a Home should not require you to go to the Google store for FW; it is only for the app software you need to do this, and I don't know about your phone, but my phone shows me all the apps that have a new version when I enter the store and then click Update All.