They have a similar use when used to mean “evaluate somebody/something/some situation.” I would say that “assess” relates more to the process of evaluating, and “rate” relates more to ranking somebody/something based on the results of that evaluation. Example: I administered several tests and performed an interview in order to assess the applicant’s technical skills. Based on that assessment, I rate him in the top 10% of our job applicants.”

In what context? For one thing, they are different tenses...