The stamina display shows players' remaining combat stamina. This is not related to sprinting stamina/exhaustion.
Combat stamina depletes with each melee action performed. When players run out of combat stamina, their melee attack speed slows significantly, though the amount of damage from each attack remains the same.
Sprinting stamina (exhaustion) is not part of the stamina display. While both regenerate over time, sprinting stamina cannot regenerate if overall stamina (combat) is also depleted, and vice versa.