From my understanding both types of attack, collision and birthday, are based on the principle of two randomly/pseudo-randomly chosen plaintext to hash to the same value. I don't want to launch any biased supposition, but aren't they the same?
From Collision attack wikipedia article I learned that every cryptographic hash function is inherently vulnerable to collisions using a birthday attack but in the Birthday attack article it is stated that the attack depends on the higher likelihood of collisions found between random attack attempts and a fixed degree of permutations, thus birthday attack only has this permutation plus?