Transformation is an ability to transform into another specific form. For example, Vampires have the ability to transform into bats. This is not the same as Shape-Shifting. With shape shifting one can take the form of whatever they desire, but transformation is generally one specific form, such as a human turning into a werewolf. Zan and Jayna, better known as the Wonder Twins from the JLA, are considered shape-shifters, as they can take a number of forms, but their shape-shifting is a bit more limited, since they can only shape-shift into various forms of water and animals. Therefore, their powers could also be described as a type of transformation.
Also, transformation isn't always a super power. The word "transformation" can also refer to someone altering something about themselves or something else being altered in some way. For example, when Clark Kent takes off his glasses and puts on his Super-Suit, he is "transforming" into Superman, and when Billionaire playboy Bruce Wayne puts on his Batsuit, he is transforming himself into Batman. Furthermore, when Julius Caesar became the dictator of Rome, the Roman Republic was "transformed" into the Roman Empire.
Some characters have the ability to transform other characters into something. For example, a vampire can transform another person into a vampire, just like Gentleman Ghost can transform people into ghosts.