thunderbolts

yes

Actually, isn't it the case that thunderbolts actually start from the ground (or sea) and travel upwards some of the time?

For sure:

Many times but not always...it can be cloud-to-cloud. The lightning generates from a potential voltage differential and contrast of temperatures. However, that's a gross over-simplification. For greater details, take a look at the following link:

http://science.howstuffworks.com/nature/natural-disasters/lightning.htm