I think of psychological testing as more quantitative or numerical-related than assessment because its purpose is to evaluate the condition of a person based on a standardized set of tests usually inform of checklists, rating scales, or questionnaires (Koscielski, 2021). These tests were created to evaluate test takers based on a well-researched, usually applicable for all or for the target group, and credible guidelines. Meanwhile, psychological assessments, based on my previous knowledge and on articles, were more qualitative in form for it may include narrative interviews, clinical interpretations, and patient's life history (American Psychological Association, 2013). Assessments like psychological reports were commonly used by psychologists and psychiatrists to come up with a diagnosis and effective treatment plan. From the meaning of the word "to test" and "to assess" we could actually understand the difference between these terms, one is to confirm something using a set guidelines that already gives a specific result, and the latter usually requires an interpretation from a trained professional and his/her clinical discernment.
References:American Psychological Association. (2013, November 10). Understanding psychological testing and assessment. http://www.apa.org/topics/testing-assessment-measurement/understanding
Koscielski, N. (2021, April 19). Psychological tests and measurements. https://www.lib.sfu.ca/help/research-assistance/subject/psychology/psychological-tests