Training for strength and training for size (hypertrophy) differ in training volume, training intensity, and rest period between sets. Training volume is the number of reps per set you do in a workout. Training intensity refers to the weight you lift. And the rest period is the time you give the body to recover between sets.
To increase the muscle size, you need to increase the training volume and decrease the intensity. In other words, you need to do more reps per set of each exercise compared to the strength training. And you have to lift enough weight to build muscle mass, but the weight you lift for muscle size should be lesser than the weight for muscle strength. The rest period between the sets and exercises is 1 to 3 minutes in hypertrophy training.
Otherwise, to increase muscle strength, you need to reduce the training volume (the number of reps per set) and increase the training intensity by lifting heavier weights. This means the rest period between sets and exercises has to be longer (3 to 5 minutes).
For most athletes, it is recommended a proper combination of strength training and hypertrophy training. But if you need to specialize, make sure your training volume, training intensity and rest period between sets are the right ones for your goals.