The algorithm is the same. The website provides a shared secret key, which you scan in the form of a QR code when you set it up for the first time. The authenticator uses that key, along with the current time, to generate a code. The website does the same thing to see if the code matches.
that is a heavy argument, I must admit. Well I see, that I learned something new today and I'll give it a try, thank you guys for this info
it is interesting to find something new and useful
The biggest problem with Google Authenticathor is that you will need to manually back up every account in another device, or save the keys offline (manually as well).
If you do not save your 2FA in one device, than save on another, for every website, you will be depending 100% on your device. If you lose the device, you will lose the access to your accounts (all of them).
I wrote about it here. Why you shouldn't use GA, or use it very carefully
https://bitcointalk.org/index.php?topic=3178131.0