Your deltoids are formed of 3 heads:deltoid anatomy
1) The lateral (medial)
2) Anterior (front)
3) Posterior (behind).
Using the shoulder press will target all 3 heads, however the anterior and lateral heads will be used most.
On the upward pressing movement the anterior head will take most of the weight when the load is focused in front of your centre of gravity.
The lateral head is used to help lift your arms out and back in while performing the movement but is also largely involved in the strength and balance of pressing above the head.