Calling time-sharing “PaaS” makes essentially the same mistake as calling pre-IaaS systems “cloud”.
First, that’s not what they were called at the time.
Second, those older systems aren’t what either term actually refers to.
(Selling time on a mainframe would be closer to IaaS than PaaS anyway - in fact IBM’s VM/CMS even used the VM abstraction, which compute in most IaaS environments depend on.)
Your position only works if you ignore the actual extant definitions of what “cloud” or “PaaS” actually refer to.
We have, according to another commenter, what cloud actually refers to: "Cloud kind of means that it's a service hosted somewhere on the Internet, that you don't control directly"
Which is what, back when network diagrams were still cool, would have been drawn as a a cloud — something that your network depends on, but something whose details don't matter. And what one would have called a cloud if they were talking about said diagram.
The word didn't magically appear out of nowhere. These services were named cloud services because that's what name we had already reserved for them.
First, that’s not what they were called at the time.
Second, those older systems aren’t what either term actually refers to.
(Selling time on a mainframe would be closer to IaaS than PaaS anyway - in fact IBM’s VM/CMS even used the VM abstraction, which compute in most IaaS environments depend on.)
Your position only works if you ignore the actual extant definitions of what “cloud” or “PaaS” actually refer to.