Hey Zachariah, static friction is an interesting problem! I know it's static friction because μs is different than μk. Have you ever noticed that cars behave differently when the tires grip the road vs. when they skid? That's because μs is different than μk.
As for your question, notice that static friction only occurs when the object is not moving. But, if a force is applied to an object, it's supposed to start moving, right? So what gives?
The answer is that static friction creates an equal and opposite force that opposes any attempt to move the object, but friction can only oppose small forces. If a big force tries to move an object, then the static force can no longer oppose the big force and the object will begin to accelerate. Accordingly, the equation only provides for the maximum possible static frictional force.
