A Birthday attack is usually applied to the probability of two different messages using the same hash function producing a common message digest.
The term “birthday” comes from the fact that in a room with 23 people, the probability of two of more people having the same birthday is greater than 50%.
Linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. Attacks have been developed for block ciphers and stream ciphers. Linear cryptanalysis is one of the two most widely used attacks on block ciphers; the other being differential cryptanalysis.
Differential Cryptanalysis is a potent cryptanalytic technique introduced by Biham and Shamir. Differential cryptanalysis is designed for the study and attack of DES-like cryptosystems. A DES-like cryptosystem is an iterated cryptosystem which relies on conventional cryptographic techniques such as substitution and diffusion.
Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in an input can affect the resultant difference at the output. In the case of a block cipher, it refers to a set of techniques for tracing differences through the network of transformations, discovering where the cipher exhibits non-random behaviour, and exploiting such properties to recover the secret key. Source:
KRUTZ, Ronald L. & VINES, Russel D., The CISSP Prep Guide: Mastering the Ten Domains of Computer Security, John Wiley & Sons, 2001, Chapter 4: Cryptography (page 163). and http://en.wikipedia.org/wiki/Differential_cryptanalysis