No, they are not the same. But you also cannot currently enroll in 2 step verification. The only people who can use 2 step verification are those who were already using it prior to iOS 11 (I think that was the time frame) and have not changed it to 2 factor authentication.
So if the OP enrolled in anything in the past two weeks, and got an email about it with a link to opt out, it has to be 2 factor authentication. You can no longer add 2 step verification to any AppleID.
Any legacy user with 2 step verification who enables 2 factor authentication on a new device is automatically un-enrolled in 2 step verification and cannot go back to it.