SAAS isn't about subscription perse although they have them of course. Its about "not needing to take care of". It's software on "someone else's computer" just as with public cloud. In a SAAS construct a provider does the hosting, computing, connection, install, configuration and maintenance. Absolving clients from that burden.
Comparing proprietary desktop applications (even with a subscription) with FOSS alternatives is useful, it's just not SAAS.
My understanding is roughly, for example:
Some caveats: Word handles spellchecker in their cloud and clippy 2024 (Copilot) integration blurs the line.