Locking out takes most of the tension off the muscle. Not-locking out makes the set a little harder so you won't rep as much with a given weight. It might also be a little easier on the joints since they don't have to hold all the weight directly.
Not going all the way down, IMO, is a good thing. In my experience bottoming out on shoulder press IS hard on my shoulder joints. If you want a larger range of motion, something like the 'Arnold' press is probably a better choice.