With the first meaning, 'out' just suggests that a greater selection is available, I think. If I were offered 2 pens, I would be asked to pick one, not pick out one, but if there were 10 pens, both pick and pick out are common, while if there were 100 pens, I think pick out would be usual.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.