Multi-factor authentication (MFA) is an authentication method in which a computer user is granted access only after successfully presenting two or more pieces of evidence (or factors) to an authentication mechanism: knowledge (something the user and only the user knows), possession (something the user and only the user has), and inherence (something the user and only the user is).
Two-factor authentication is a type, or subset, of multi-factor authentication. It is a method of confirming users’ claimed identities by using a combination of two different factors: 1) something they know, 2) something they have, or 3) something they are.
A good example of two-factor authentication is the withdrawing of money from an ATM; only the correct combination of a bank card (something the user possesses) and a PIN (something the user knows) allows the transaction to be carried out.
Two other examples are to supplement a user-controlled password with a one-time password (OTP) or code generated or received by an authenticator (e.g. a security token or smartphone) that only the user possesses.
Two-step verification or two-step authentication is a method of confirming a user’s claimed identity by utilizing something they know (password) and a second factor other than something they have or something they are. An example of a second step is the user repeating back something that was sent to them through an out-of-band mechanism. Or, the second step might be a six-digit number generated by an app that is common to the user and the authentication system.