Yeah, it's just browser-software rental.
If "service" made the difference, desktop and mobile-native software providers wouldn't offer services, like hosting and support, but they do.

SaaS is just easier to bugfix universally, without having to inform anyone, that you messed up. Stealth updates. 🤣 

 I've worked on desktop (Linux and Windows), mobile (Android), and browser-based. Never Apple, as the sales guys all had Apple-Everything and they would test. 

 Easier to fix the bugs that wouldn’t have been introduced had they developed for cross-platform desktop. 

 Much more control, from the desktop.