Software stocks have sold off on fears AI could eat into so-called software as a service, or SaaS, business models.

As their stocks tank, software makers are rebranding themselves as A.I. innovators. Sparkle emojis are everywhere, but some efforts have been more successful than others.

The carnage reflects growing nervousness over the future of the software industry in the age of artificial intelligence. The value of listed American enterprise-software companies is down by 10% over ...