Chronometers

It depends when the watch was made.

Prior to the early 1950’s, there was no centralized independent testing facility in Switzerland. Watches marked “chronometer” were generally tested by the manufacturers. Sometimes a certificate was included, sometimes not.

Later on, the major companies got together and set up a facility to conduct movement testing and issue appropriate documentation to the manufacturers to show their watches met agreed-upon standards to be called a “chronometer”. These standards have varied over the years, and are much tighter for quartz chronometers.

In the US, there was some controversy as some importers included the word in their company name. As in “The Ulysse Nardin Chronometer Co. Inc.”They would use the full company name on the movements and dials, although that did not necessarily mean that the watch was tested or actually met any sort of standard. Some were even marked as “unadjusted” to save on customs. Very confusing.

At some point, the FTC stepped in and declared that sort of thing as misleading advertising.

And this is just a start!
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You may also be interested in reading about the observatory chronometer competitions, where watch manufacturers sent their best watches to compete.