Laura, That's an English Style Windsor rather than American. Sort of a hybrid as most English ones are heavier and bulkier than yours. I specialize in Windsors and haven't seen one like that before. Might be difficult to find. Duane Collie

They're bar stools, right here at Houzz - [https://www.houzz.com/products/kings-bar-height-barstool-white-with-metal-studs-set-of-2-prvw-vr~32311463[(https://www.houzz.com/products/kings-bar-height-barstool-white-with-metal-studs-set-of-2-prvw-vr~32311463)

Check a few sites: https://franceandson.com/, https://www.1stdibs.com/, and https://www.allthedecor.com/decor/, One of the three will have it or probably be getting something very similar soon, france and son can have some issues with shipping, so just ask about it first before you buy, I bought some lamps there and they were fine but had to cancel a table because of an issue with shipping meaning they wouldn't ship large items, but maybe that's changed by now, allthedecor is going to carry similar items and should either have them now or soon...best of luck!

Don’t know your budget. Most companies make them. Check Rowe. (Unless you are actually looking for barrels that were turned into swivel chairs?! They were a thing back in the 1950s!)