From what I understand, ActionScript (.as files) and Action Panel (F9 embedded in Flash) are completely different. If so, which one is better used for game programming and which one is more powerful? Can ActionScript do everything that the Actions Panel can do?
they're different but not completely different.
actionscript code can be placed in the action panel or it can be in stand-alone .as files. there's no difference in the code used in an .as file vs code in the action panel.
and i'm not sure powerful is the right word, but code in stand-alone .as files can do everything code in the action panel can do but not vice-versa: you can create classes in .as files and you can't do that in the action panel.