Definitions vary all over the place, so your results may vary. This works for me.
Hosting - running and maintaining a computer system on someone's behalf.
SaaS - Software-as-a-Service is a model of software deployment whereby a
provider licenses an application to
customers for use as a service on
demand. One example of SaaS is the
Salesforce.com CRM application.
IaaS - Infrastructure-as-a-Service is the delivery of computer
infrastructure (typically a platform
virtualization environment) as a
service. Rather than purchasing
servers, software, data center space
or network equipment, clients instead
buy those resources as a fully
outsourced service. One such example
of this is the Amazon web services.
PaaS - Platform-as a-Service is the delivery of a computing platform
and solution stack as a service. It
facilitates the deployment of
applications without the cost and
complexity of buying and managing the
underlying hardware and software
layers. PaaS provides the facilities
required to support the complete
lifecycle of building and delivering
web applications and services. An
example of this would the GoogleApps
So, whether its SaaS, IaaS, Paas - its all "hosted" - that is, running somewhere other than on your hardware, and you pay for it (of course, there are hybrid solutions that incorporate your hardware + their hardware, but let's keep it simple for now.)
How you pay - per use, monthly, quarterly, annually - is a condition defined by the provider and not a deciding factor on what type of provider it is.