When you are stronger, more volume can be performed with the same weights. And greater volume with greater weight eventually leads to greater size.
More weight can be used on isolation exercises. If you front squat 500 pounds, odds are you can do heavier leg extensions than if you only squat 300 pounds.
The two identified factors for increasing strength are increased neural factors: increased coordination of the movement and an increase in muscle size. In other words, strength equals size and vice versa.