Well...they have nothing in common really.
The term "psychoanalyst" refers to a doctoral level professional (MD or Ph.D.) who practices the orthodox form of psychoanalytic psychotherapy practice by Freud. The couch, free association, dream interpretation....the whole shabang. Not alot of these guys left anymore, but they are around here and there. Many practitioners still use psychoanalytic principles in their therapy and/or follow a more liberal form of psychoanalysis (known as psychodynamic psychotherapy) in their practice, but the old-school orthdox analysts are few and far between these days.
The term "psychometrist" describes a BA or MA/MS level progfessional who administers (and usually scores) psychological and/or neuropsychological tests. I did this for 2 years in a outpatient neuropsychology clinic before I sought my Ph.D. Psychometrists are usually suprvised by a clinical psychologist who does the higher level interpretation and formal report writing of the test results.