It isn't just ring signatures, it is a combination of techniques involving a particular construction of ring signature, breaking amounts into equal denominations for mixing, and stealth addresses (including making outputs of a transaction unlinkable with each other) that comprise the CryptoNote application of the math to the practice of cryptocurrency (saberhagen white paper). The same methods with minor variation are used in Shadow. The most recent Shadow uses Adam Back's modified ring sigs (approaches 1/2 size with large mix factors), so it does deviate from CryptoNote there.