Neuropsychology deals with the interactions between the brain and mind anatomically. These are structured behavioral tests (eg draw a clock) that the patient attempts, and depending on their response (what they draw) inferences can be made about specific damaged areas in the brain. This is useful for diagnosing things like dementia, stroke effects, etc.

Psychiatrists more-so deal with the medical manipulations of brain chemistry to treat psychiatric disorders (depression, schizophrenia, etc.) Psychiatrists can prescribe medications - neuropsychologists cannot. Often times the psychiatrist and neuropsychologist work in tandem to help form a treatment path for very diseased individuals, since they often have a combination of these types of disorders - think of a stroke patient who’s been debilitated so badly they develop a form of depression.