Tableware sets in the US commonly come with at least two different sizes of spoon. These usually bear no relation to the "measuring spoons" used to measure volume, though they are handy for stirring tea or eating soup (for the small & large spoons, respectively).

For people who cook in the US, a set of "measuring spoons" is a very common kitchen tool.

"Teaspoon" and "Tablespoon" are units of measurement of volume, not bits of silverware. "Tea spoon" and "Table spoon" or "Soup spoon" are pieces of silverware, not units of measure!

Seems like a weird statement. As someone who cooks and bakes, I use teaspoons all the time. Teaspoons for certain spices and seasonings are extremely common in recipes

Yeah, this isn't true. A teaspoon is a standard unit of measurement in US cooking.