Google rolled out a new look and feel for two-factor authentication earlier this year, and soon it will encourage people still using the text message-based system to try it out. Google Prompt pops up a notification on authorized mobile devices with information about a login attempt, including what device it's coming from.
It's easier to understand than an SMS, sent over a secured connection and isn't as susceptible to phishing. Also, it avoids the problem of someone taking advantage of phone company customer service to hijack your phone number and intercept SMS verification, which has happened in some cases. On the downside, it requires a data connection.
As a result, starting next week, SMS two-step verification users on Google will see an invitation to try out the new system, although anyone with a security key will not. On Android the system is built-in, but iOS device users will need to have the Google Search app installed.