How do I explain Swiss Cheese to Ukrainians?

My wife is making Reuben sandwiches after trying the most heavenly Reuben in Cracker Barrel when we visited the US. The conversation goes like this:

– What type of cheese goes on them?

– Swiss?

– Huh?

– Swiss. “Shvaitsarski.” You know.

– They make lots of different cheeses in Switzerland.

Apparently, there’s no conception of an individual flavor of cheese called Swiss in Ukraine. Wikipedia sheds some light:

Swiss cheese is a generic name in North America for several related varieties of cheese, mainly of North American manufacture, which resemble Emmental cheese, a yellow, medium-hard cheese that originated in the area around Emmental, in Switzerland.

Also, this is cool:

Swiss cheese without eyes is known as “blind”. . . .

In general, the larger the eyes in a Swiss cheese, the more pronounced its flavor because a longer fermentation period gives the bacteria more time to act.[9] This poses a problem, however, because cheese with large eyes does not slice well and comes apart in mechanical slicers. As a result, industry regulators have limited the eye size by which Swiss cheese receives the Grade A stamp.[10]