The Commodity Exchange Act (CEA) excludes security-based swaps (other than mixed swaps) from its definition of a swap, and the Securities Exchange Act defines these transactions as security-based swaps. An equity swap that tracks the price of one stock is based on a single security, so it falls into this category. A swap that is not based on these things, such as an interest rate swap, is not a security-based swap. A transaction that meets the definition only because it refers to certain exempted securities is excluded, unless it has the character of an option.
A transaction that is a security-based swap and is also based on the value of something else is called a mixed swap, and the rules of both the CFTC and the SEC are relevant to it. The article "The Roles of the CFTC and SEC" explains how they are divided.