There is a lot of confusion about how software-as-a-service (SaaS) relates to cloud computing.

Although both can be somewhat defined according to technological and business perspectives, SaaS is best characterized as a business model for delivering and deploying software applications, whereas cloud computing is a general concept based on the abstraction of infrastructure. Therefore, cloud computing encompasses SaaS, although I would rather say that SaaS relies on cloud computing.

Wikipedia defines cloud computing as [extract]:

The cloud is a metaphor for the Internet, based on how it is depicted in computer network diagrams, and is an abstraction for the complex infrastructure it conceals. [...] Cloud computing is a general concept that incorporates software as a service (SaaS), Web 2.0 and other recent, well-known technology trends, in which the common theme is reliance on the Internet for satisfying the computing needs of the users.