Two coefficients share one surface. $\mu_s$, the static coefficient, governs things at rest; $\mu_k$, the kinetic one, governs things already sliding. And they behave differently in a way worth a mark every year: $f_{s,\max} = \mu_s N$ is a ceiling, not a fixed charge. Lean on a filing cabinet with 20 N and static friction pushes back with exactly 20 N; lean with 60 N and it pushes back with 60 N. It matches you, newton for newton, until you ask for more than $\mu_s N$ — and at that instant it has nothing left, the cabinet breaks loose, and $f_k = \mu_k N$ takes over as a fixed toll for as long as the slide lasts. Since $\mu_k$ is usually smaller than $\mu_s$, the shove gets easier the moment it starts. That is the lurch you feel moving furniture.

There is a second way to measure $\mu_s$, and it needs no force meter at all: tilt the surface until the object just begins to slide. At that verge the down-slope drive $mg\sin\theta$ exactly equals the ceiling $\mu_s\,mg\cos\theta$, the mass cancels off both sides, and what is left is the angle of repose: $\mu_s = \tan\theta$, mu-s equals tan theta, with $\theta$ the steepest angle in degrees the surface can hold. The mass cancelling is not a convenience — it is the physics. A sand grain and a boulder tip at the same angle, which is why every gravel pile on Earth wears the same slope.