Exertion.
Even the slightest bit of exertion (such as standing up) will cause a slight quickening of the pulse. The amount your pulse quickens depends a lot on your level of physical fitness.
I often wonder this as well. My laying down rate is well within the 60 to 80 but standing I go higher to about 80 and then walking runs me like 90. I'm in pretty good shape and always wondered if the increases were normal. Just as an FYI, I am a 28 year old female.
A normal resting heart rate is 60-80, but there's flexibility in those numbers. As for standing heart rate - I think it would depend on the person. 120 is probably too high, 50 is probably too low.