Delusional disorder is a fixed non-bizarre thought. non-bizarre means that the thought is possible but it's not true. e.g patient think that people are after him to kill him.
It's usually a single delusion and does not impair patient functioning significantly.
Brief psychiatric disorder is a full psychotic dimension but for less than 30 days. The delusions are usually bizarre which means they are not possible such as out of space aliens will come and take you. Usually the patient has multiple delusions not only one and it impairs domestic and social functioning significantly.