The difference is that they usualy plan for a longer time, sometimes for generations, while the usual CEOs plan very short term, because they don't care what happens with the company after them. Family owned business don't have to give out part of their earnings every year, so it's not that big of a problem if they have little earnings in a year, while the market share of a normal Company will immediately fall. So there actually is a huge difference.

That aside I don't know why they market it like that. I think it just sounds more trustworthy.

My employer says this as a way to show they won’t ever sell out.

Looking at the trust, they aren’t allowed to sell out lol

If it's a gas station franchise I'm not too concerned. If it's an international Fortune 500 insurance company I'm starting to worry.

Family owned to me sounds like:

Nepotism abounds probably, half the shareholders inherited wealth and didn't earn it, so they probably don't know how to run the company as well as the people who built it, enjoy the "we're all a family" talk, while your manager hires his son timmy to be your boss despite zero experience or qualifications.

Walmart

As long as it's a small business, that's fine. If you're a big business, you should try to think back to what happened during the French Revolution.