Honest question: what should someone call themselves when they've started, for example, a restaurant, two software companies, and a property management firm?

I'd call them a douche bag. Seriously this isn't something you want to advertise even if it's true. Stay down to earth and play down your successes especially if the person you're talking to is less successful then you.

Did Steve Jobs call himself a serial entrepreneur? True success advertises itself.

A business owner? If you've found success, you own a lot of businesses. If you haven't, you own one even though you have started more than you currently have. You're still just a business owner.

"Business owner" implies they currently have sole or majority ownership in a business, but with many companies both big and small, multiple people have ownership stakes. Founders also often don't retain an ownership stake forever, since many businesses change ownership during their lifetimes, and others shut down.

So, in my example above, what if the person only retains a minority ownership stake in the restaurant, sold the two software companies, the property management company failed, and they are now working on a new company of any kind? Does "business owner" really accurately describe what they do?

Note that if you think this kind of example is unusual, in my experience it's relatively common for people who build companies to do so in different domains, either simultaneously or at different stages in their careers.