Difference between primary key and unique key

I'm using a MySQL database.

In which situations should I create a unique key or a primary key?

Primary Key:

• There can only be one primary key constraint in a table
• In some DBMS it cannot be NULL - e.g. MySQL adds NOT NULL
• Primary Key is a unique key identifier of the record

Unique Key:

• Can be more than one unique key in one table
• Unique key can have NULL values
• It can be a candidate key
• Unique key can be NULL ; multiple rows can have NULL values and therefore may not be considered "unique"