"I don't think that's right what you've put about tethering."
It is.
When you're camping your phone, as you say, turns into WIFI. So you've got WIFI.
When you're at home you get this:
Internet Broadband Router Gadget
When you're camping you get this:
Internet 3G Mobile Phone Gadget
There's the WIFI connection, the link between your gadget and the gadget that talks to the internet. And you'll probably find that the WIFI connection at home between your gadget and your router is exactly as fast as the connection between your mobile and your gadget when your camping. In fact I'd go as far as to guess that when your camping that WIFI connection will actually be quicker than you get at home as you'll have your phone right next to your laptop and there won't be lots of other wireless signals floating around interfering with it..
However your broadband connection at home is much quicker at talking to the internet than your mobile phone is, but still much slower than your WIFI. So the "speed" you "feel" is the broadband connection.
It's the same when you're out and about, your WIFI connection when you tether will be many many times faster than your 3G connection, so the "speed" you feel is your 3G connection.
So home will seem faster because broadband is faster than 3G, it's nothing to do with the WIFI.
So yes it's WIFI, and if you're somewhere where you can't have WIFI for some reason (interference? e.g. a hospital?) then you will not be able to tether. That WIFI "bridge" between your gadget and the device providing the internet connection (phone or modem) is still there.