ICD is the only international classification. It is used by every country in WHO. This means that every disorder in DSM has to have an equivalent coding to it. Both nosologies are in line with one another, despite having different naming conventions and diverging criteria.

The synchronisity is achieved from DSM to ICD through specifiers and subtypology, and reverse maps via domain criteria from ICD to DSM. With respect to personality disorder, the FFM is often the middle man used to achieve that, because both models align to it.

Keep in mind that under DSM the categorical model is a legacy hold over to DSM-4, the preferred nosology since 2013 is AMPD (the DSM equivalent to ICD-11 dimensional model).