You can install Go apps even without the Go Edition of Android.
The differences between Google Go and the normal Google app are: (as I have experienced, anyway)
1. No 'hey Google' support. You have to open the companion app 'Google Assistant Go,' another app install entirely, to get the functionality of the Assistant, but even with that, there is no 'Hey Google' support with Go apps.
2. UI is a basic, bland bright white, hard on my eyes. It has hardly any support for 'cards' or 'the feed'. It won't remember where you parked, for example.
3. Its storage and RAM footprint are 1/3 what the normal Google app is.
4. Google Assistant Go, its companion app, won't accept many of the commands that the full Assistant does. You can't control smart home devices, control Wifi or Bluetooth, or find a song via song search. It's essentially the modern version of 'Google Now' in that it is basically voice search with few features.
If you needed to use those to overcome a storage issue (I just turn updates off and stick to what comes with a device, works perfectly fine--not like they're actually adding things to it these days!) you'd have to uninstall updates and disable the Google app itself in settings. Some modern Android versions don't uninstall the updates/clear data by 'disabling' the app anymore like they used to, so you won't get your space back on Android 12+ just by disabling the app.
BTW, Play Store is a bug-ridden mess. A lot of the times it claimed I had insufficient storage to install/update an app it was wrong. A lot of times it deemed a specific app 'incompatible with my device.' I've proven it wrong both times by sideloading the *.APK of the app I attempted to use Play Store to install for me. A lot of times using an app store is more frustrating than doing things the geeky way.