2-step verification is a form of two-factor verification where you are required to tap on a push notification on your primary mobile device to verify your identity.

SMS requires you to receive a one-time passcode through a text message and then enter that code into your secondary device to verify your identity.

For SMS, you need to be connected to your mobile network in order to receive a text message. For 2-step verification, you need a Wi-Fi or mobile network connection.