Yup. These calipers that measure to .0005 of an inch only show hundredths of a mm (10 microns).

As for language, "thou", short for thousandths of an inch, is kind of the base unit in imperial machining. That's why the next one down is "tenth" in the vernacular. It's very confusing because 100 thou is one tenth of an inch, but you'd never call it a "tenth" even if "inch" is implicitly the base unit. Also confusing is that there are SI prefixes for all of these things, but they aren't in use. (Why not "milliinch"?)

Finally, one more advantage of the metric system; to measure 1 micrometer, you need a tool called a micrometer. That's easy to remember!