Yes. A fan design can be optimized to deliver very good air flow against significant backpressure (air flow resistance) such as from a radiator or finned heatsink, OR for even greater air flow against very little resistance such as general case ventilation. Your two terms are both for the first case; ones for low backpressure are usually called Air Flow fans, sometimes Low Pressure fans. There are some on the market also that are compromises designs aiming for one fan that can do both types of jobs reasonably well, if not really optimal for either situation.
Yes and no. Static pressure as such is a general term that can cover any fan with blades designed to combat resistance. This can include the extreme rpm fans made by Delta that have such high rpm (some are upwards of 8000rpm) that they create massive amounts of SP.
Pressure optimized fans are designed to do just the opposite, create as much SP as possible, with the lowest viable rpm, while still maintaining enough cfm to get the job done.
To put it bluntly, a Pressure Optimized fan is just a more specialized form of static pressure fan.