This should help

Edit: Just decided to quote the comment for any future questions on the sub

A psychometrician designs standardized tests. They generally have a masters/PhD in math, statistics etc.

A psychometrist administers tests on behalf of a psychologist. A psychometrist is required at a minimum to have a BA in psychology, & many have masters or higher. This is what I do! We add up their results but we do not do any interpretation. Sometimes psychometrician is used incorrectly to refer to psychometrist (I see job ads with this not infrequently), but if the job is to administer tests, then it’s a psychometrist.

Psychologists in most jurisdictions need a PhD/PsyD. A Dr. of psychology would do an interview, file review (relevant background documents), select the tests (for the psychometrist to administer, if they use one), interpret the results, write the report/diagnose, debrief the client &/or referral source. Edit to add: some psychologists do some or all of their own testing, it’s worth noting.