TOTP works without an internet connection. It’s nothing more than a “shared secret” with a timestamp.

Both the application and the server have the same string through which token based on the “current time” is generated.

So the fact that it works offline is both an advantage and a disadvantage. The advantage is that it always works. Even if your mobile service provider is experiencing an outage and you don’t have WiFi. All it takes is that your watch is working properly. (or at least equal to the hour of the service you want to log in to)

The drawback is that there is no verification that you have entered the code. If you somehow manage to get your shared secret, no one will be able to see it. Another drawback is that it is not a shared secret at all. Both sides have the same string stored. Undivided. Just plain code, otherwise it won’t work.

The advantage of SMS is that it is recorded. However, you can then see where the text message was sent. Even if someone else temporarily took over my SIM/phone number (which is the drawback), this would at least be provable afterwards.

With TOTP, you will never know anything, because it is offline.

Therefore, both systems have advantages and disadvantages.