What is the difference between a primary key and an index key?
When do I use each?
A primary key is a special kind of index in that:
You tend to use the primary key as the most natural unique identifier for a row (such as social security number, employee ID and so forth, although there is a school of thought that you should always use an artificial surrogate key for this).
Indexes, on the other hand, can be used for fast retrieval based on other columns. For example, an employee database may have your employee number as the primary key but it may also have an index on your last name or your department.
Both of these indexes (last name and department) would disallow NULLs (probably) and allow duplicates (almost certainly), and they would be useful to speed up queries looking for anyone with (for example) the last name 'Corleone' or working in the 'HitMan' department.