In 1969 AI pioneer and Stanford big brain John McCarthy proposed computing delivered as an on demand utility. Comparable to the electrical grid.
Does that sound familiar?
It does to me and through the sweating masses of people yelling about SaaS, PaaS, IaaS and MyaaS, UraaS, TheireaaS, all thinking like they've discovered something which previously never existed, we find it all just the same generic auto-tuned to within an inch of it's life technological pop music that's always been there.
You can add aaS to whatever you want be that someone providing you with compute, storage and bandwidth in their data centers or someone providing you with an entire closed application execution environment which they own but onto which you deploy your customisations but it's the same old singsong as it was in the days of Service Bureaus in the 70's, Application Service Providers in the bubble years of the late 90's and Cloudy aaS (as a service) providers today.
That's close to 40 years of nothing more than buzzword rebranding with people standing in rooms thinking up of new names and agreeing they're new ideas. It all comes back to the software or hardware Mainframe in your data center or the Skyframe in someone else's. The resources you own or the resources you rent time on.
Extending the three letter acronym to four letters is the only innovation that appears to have occurred in this domain.
Go faster stripes would have looked better.