Stride length is more important than stride rate for increasing distance running speed. When you increase your pace from a jog to a run to a fast run, stride length increases more than does stride rate, until you’re sprinting very fast, when stride rate begins to dominate further increases in speed. Stride length explains much of the difference in speed among distance runners.
Research has shown that, up to about 3:50 per mile pace, running speed is increased by increasing stride length by the plantar flexor muscles (gastrocnemius and soleus) producing more force against the ground. At very fast speeds, the speed of muscle contraction is so fast that there is not enough time to produce a lot of force, and plantar flexor peak muscle force begins to decrease. (The force-velocity relationship dictates muscle force production; the faster the speed of contraction, the lower the force.) The primary strategy used to increase running speed faster than 3:50 per mile pace changes from increasing stride length to increasing stride rate. Specifically, the hip muscles (gluteus maximus, psoas, and hamstrings) become prominent players to quickly accelerate the leg forward during the swing phase.
Unless you’re a sprinter, don’t focus on increasing stride rate (unless you land with your foot far out in front of you, in which case it would be beneficial to take quicker steps), and instead focus on increasing stride length by increasing hip extension and applying greater force to the ground at push-off.