It’s a broom, but it’s not. It’s a mop, but it’s not.
It’s broom shaped, but instead of bristles, it’s moppy stuff. But you don’t use a bucket, you use it like a broom to pick up dust and pet hair off the floor.
I’ve never seen one in the supermarket, but I’m guessing you must be able to get them from somewhere! I wonder if they’re used commercially more than domestically?
Grandma loved hers, mom couldn’t be bothered. With hardwood floors, I’ve now sided with Grandma. It’s bigger than a Swiffer and gets the job done in half the time. When I’m done, I stick it out the window and shake the dust off outdoors.
ETA: another advantage over the Swiffer is that there’s no paper cleaning rag to stuff into little clips or holes. It’s always ready to go, with no waste. And you can take the head off and launder it when it gets too soiled to shake off.