Brake-component function matters because identical symptoms can arise at different stages. A hard pedal can involve assist; a sinking pedal can involve pressure containment; pull can involve friction, release, tires, or suspension; fade can involve pad material, rotor temperature, fluid, or load.
Knowing the job of each component turns parts replacement into controlled diagnosis. It also prevents fitment shortcuts: master-cylinder volume, caliper piston area, rotor radius, hose routing, ABS valves, sensors, and parking hardware are selected as a system. The goal is not merely to install something new, but to restore force, balance, thermal reserve, redundancy, warnings, modulation, and hold.