The focus of the assessment would depend on why the client is seeking OT treatments, and that would in turn be guided by the setting (i.e., inpatient hospital vs. school-based would have very different assessments). To answer your question more directly, the kind of assessments can range from cognitive level and manual dexterity to the level of assistance needed to do activities of daily living and how satisfied the client is with the direction of his or her life. In other words, from very specific to kind of general, from addressing the mind to addressing the body.
They determine a deficit and that's usually measured as compared to the population (e.g., patient is very low on this measure compared to someone his age) or compared to a criteria (e.g., patient is a level 2 on a 1-5 scale on this measure).
Other assessments just guide the focus of the intervention to determine what to do first and what to work on second according to the client's preference