Someone might have addressed this in an earlier post, I only read the OP.
I took some courses on muscular anatomy and neuromuscular physiology, so here's my quick breakdown on the difference.
A major difference between the pullup and the shoulder press is the effect on the scapula. There are other parts at work, for sure, but the main difference is that during a shoulder press you are superiorly rotating the scapula, whereas during a pullup you are inferiorly rotating it.
Stick out both your hands in front of you as if you were to give a double high five, thumbs perpendicular to your fingers. This is the starting position for your scapulas before a shoulder press. Now rotate both your hands outward, so that you end with fingers pointing toward each other and thumbs pointing down. This is the end position for your scapula at the top of the shoulder press movement. This movement is known as superior rotation of the scapula.
These positions are reversed for the pullup. Inferior rotation.
Most people seem to think of these exercising working the shoulders, triceps, biceps, and such. But there is much more going on here. Many muscles of the posterior chain are at work to produce the scapular rotations, and they are different, and sometimes overlap as well.
I did an article on this over on RoK some time ago, I broke down the shoulder press if anyone is interested:
http://www.returnofkings.com/21112/the-b...y-exercise