Is SaaS really cloud?

I've been watching the discussions around defining cloud services for the past few years.  I think that, like several others here, that IaaS and PaaS are going to merge as the lines blur more.  But my big wonder is about SaaS?  Is it *really* cloud?

I've spent the past 8+ years in my career working for various ASPs.  I/PaaS is the next step in flexible operational environments, be they public or private.  It is the logical extension of what ASP operations personnel have been architecting for scalable, reliable computing.  Pushing the concept of hosted services, utility computing and spill-over resources to its limit has the potential to be a game changer for IT spending and management.

SaaS doesn't look new to me or even evolutionary, it merely looks like more multi-tenancy ASPs.  These aren't new, have been successful in the past.  Salesforce.com doesn't really look any different now that they claim to be SaaS than when they were a multi-tenant ASP.  I can see that an enhanced infrastructure changes the easy of scalability for a multi-tenant ASP, that was always a big problem for us.  But is it a game changer?

Is SaaS really just the ASP vendors trying to stay "relevant" in a new marketing push?  Am I missing something *because* of my background?

Comments, criticisms, complaints?