A collision attack involves finding two different inputs that produce the same hash output, compromising the uniqueness of hash functions. It enables attackers to forge digital signatures if they can find two sets of data with the same hash value. Birthday attacks, named for the statistical phenomenon called the birthday paradox, are a type of collision attack, but they specifically refer to the mathematics behind the likelihood of collisions. Downgrade attacks involve forcing a system to abandon a higher security protocol in favor of an older, less secure one, thus not related to hash collisions. Side-channel attacks exploit the physical implementation of a cryptosystem, rather than directly attacking cryptographic algorithms or keys.