NW's P class is for full-fare, paid First Class. However, with NW discontinuing First Class product internationally, I'm not sure what P will stand for in the future.

Generally, airlines each have their own system of booking classes. This was designed, I believe, for revenue/yield management purposes. Each booking/fare class (should be distinguished from service class), is assigned to be booked in a certain level within each airline's revenue/yield management hierarchy. However, booking classes might not always book into the same bucket (revenue management term for fare class within the system) on all flights, or even on the same flights. Therefore, it is entirely possible to have a 2 B booking class ticket on the same flight booking in different buckets. This allows the airlines to control the seats being sold at different fare levels through adjustments anytime throughout the lifetime of the booking period.

Another point to keep in mind is that designated booking classes are not necessarily assigned based on rules or fares, but also for point of sale.

Hope that helps.