PAP (Password Authentication Protocol) - Passwords are sent in unencrypted clear text.
CHAP (Challenge-handshake Authentication Protocol) - Use of shared plain text secret such as a password. The shared secret is never sent over the network.
MSCHAP (Microsoft Challenge-handshake Authentication Protocol) - This is the Microsoft version of CHAP. MSCHAP doesn't require the server to have a copy of the user's plain text password, instead an encrypted version of the password can be stored on the server. MSCHAPv1 also supports additional error codes over CHAP.
MSCHAPv2 is a more secure version of MSCHAPv1 offering additional features such as two-way authentication and different encrypted passwords everytime the user connects.