It’s quite a bit simpler than that. Just like the Amazon echo, the Google Home uses the cloud to parse the voice input that it receives. For a home automation request it just converts that to a message format agreed-upon between SmartThings and the voice processor. It’s not completely clear yet how that message gets transferred over to SmartThings. With echo, it’s a cloud to cloud integration.
With Google home, one journalist wrote that weave was being used, but no one else has confirmed that yet. (Tech journalists do get these kinds of things wrong occasionally.)
So it could be that a person talks to google home, the audio is passed up to the Google cloud for processing, the result is passed back to google home, and then Google home passes the formatted device request over to the SmartThings hub via weave. But I doubt it.
I think it more likely that a person talks to google home, the audio is passed up to the Google cloud for processing, the result is sent cloud to cloud to SmartThings, and the SmartThings cloud passes the formatted device request down to the SmartThings hub just like all the other SmartThings cloud requests.
If somebody wants to test this, it would be easy enough – – just unplug the SmartThings hub from the Internet while leaving google home connected to the Internet and see if a Google Home request gets through. But I’ll bet a virtual pizza that it doesn’t. 
The Phillips hue bridge is an entirely different situation. They have an open API, so any device which is on the local area network can talk to it. That includes a SmartThings hub, Google home, Amazon echo, Harmony, wink, etc. The protocol there is LAN. That will run completely without the Internet, but that’s because the hue bridge doesn’t have to do any cloud processing, unlike all of the voice processors so far.
Nest offers two means of integration. The first is its own version of thread, and that’s what most of the official integrations use. But because it allows for Internet access, there are unofficial integrations, including one developed by the community for SmartThings, which are cloud to cloud. Neither weave nor Thread is required between the third-party device and nest because the message is just getting passed in the same way that a request from an app would be.
So to get back to your original question, when you have a Google home and you have a SmartThings hub and you have set them up to talk to each other you can then control some of your devices (not all) by using voice to the Google home which then passes the message over to the SmartThings hub, Then SmartThings uses any of its normal control methods to perform the request. So google home is essentially just a voice UI FromSmartThings’ point of view.
Or you can still use all your normal methods through SmartThings for controlling compatible devices.
There’s a very active current community discussion thread about Google home if you would like to talk with people who already have both devices set up or if you have more specific questions. 