Primary KEY is more of a logical thing, however Primary INDEX is more of physical thing.
Primary INDEX is used for finding best access path for data retrieval and data insertion and
Primary KEY is used for finding each rows uniquely just like in other RDBMS.
As per your question: There is no such thing as unique primary key.
Primary key is unique and not null.
Yes, for those coming from other DB background, like oracle, the concept is different.