SOA (Service Oriented Architecture) is fundamentally about enabling software to be constructed from a network of "services", so when I first encountered the SaaS (Software as a Service) acronym I assumed it was marketing hype for the same thing.
It isn't.
Software as a service is a model of software deployment very similar to the traditional ASP (Application Service Provider) model where an application is hosted as a service provided to customers over the internet. The benefit to the customer is that the burden of software maintenance, operation and support is alleviated, whilst for the service provider there is through virtualisation the possbility of applying economies of scale to the operation.
It seems to me that SaaS is just like ASP, but apparently the differences are due to SaaS's focus on the web and multi-tenant back-ends which enable greater economies of scale than ASP.
Its a pity, because I think SaaS as an acronym would have fitted the SOA space better.