What are the differences between collision attack and birthday attack? 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?
Collision attacks are attacks where success is obtained when two values obtained by some process are identical. The term is often used in the context of hashes, since collision-resistance is one of their desirable property.

Birthday attacks are collision attacks that work by the effect of chance, with the colliding values obtained by some roughly random process (as in the birthday problem).

Marc Stevens's Single-block collision for MD5 (2012) is an example of collision attack that is not a birthday attack.