Hey, Jillybean!
All three heads work in lateral raises and overhead presses. Although the primary action of the deltoids is glenohumeral abduction, the anterior head contributes to shoulder flexion, and depending on position, to horizontal adduction/horizontal flexion and medial rotation. The posterior head contributes to extension, horizontal abduction/horizontal extension and lateral rotation.
There are several reasons that overhead lifts are more difficult than anterior, lateral or posterior delt raises. First of all, all three of the delt raises stop when the shoulder is at approximately 90 degrees of flexion, abduction or horizontal abduction/horizontal extension. Overhead lifts typically progress to where the shoulder is at approximately 160-180 degrees of flexion or abduction, meaning that the distance traveled is significantly increased, therefore the amount of work done is greater in an overhead lift.
Secondly, there is something known as a length-tension curve, which basically means that there are points along the range of motion where the muscle is able to generate more force than at other points. Muscles are able to generate maximal tension in the middle of the contractile range. With delt raises, the exercise ends at close to mid range for the muscle. A good part of the range of motion of an overhead lift is well past this optimal point.
Thirdly, because of position, the involvement of other muscle groups varies when the motion gets much past the 90 degree point (flexion or abduction). When there isn't as much assistance from the pecs or upper traps, the exercise becomes more difficult.
Finally, upper body exercise that takes the arms above the heart makes it more difficult to pump oxygenated blood to the working muscles, causing lactic acid to build up more quickly. You get the burn of fatigue, which limits the intensity of the contraction.
I know I went into great detail here, but there are all sorts of reasons for why overhead lifting is harder! Hope this was helpful!
Maribeth