I have never really felt to happy with calling a webbased service for ASP (application service provider) since that is for me what it was in 2000, a client/server software distribuated using, for example, Citrix to a webbrowser.
SaaS (Service as a Software) is better name for the services of the future. Something that is build from scratch for the web.
Where I found the acronym;
'Software as a service: The next big thing?' (An article in InfoWorld 20th march 2006)