The difference between "go out" and "hang out"?

Anonymous
Alright, so tomorrow I hope to gather some minuscule amount of courage together and ask a girl out. Its been nearly a year since the last relationship (which lasted a long time), and feel like taking a leap of faith. I am not sure if she likes me back or not as we are both relatively shy and quiet people - so I can't say for sure whether she does or not. But my biggest question is: is there a huge difference between using the phrase "Would you like to 'go out' sometime?" and "Would you like to 'hang out' sometime?"

I had planned on just being direct and asking her to "go out" (considering I have a hard enough time asking anyone out)...but I was told not to do that as it would seem creepy and too forward (quote: "It would make you look like you were asking her on a boyfriend'/girlfriend date")

Is one more direct than the other?

Does one mean "dating" more than the other?

Given the fact I am unsure if she likes me or not, which one is more casual and inviting to a relationship?

Any other thoughts? I have never understood this secret language used in initiating relationships...and if it ends up the best way of resolving things is for me to literally walk up to her and say "Hey, I like you" then so be it...I just don't know what is expected honestly.

Thanks!
Updates
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(Update: I guess it should be added, that I have tried to drop some hints that I do like her already. You know, the whole catching eye thing and trying to make special considerations for her in things even if it may look a little odd)
The difference between "go out" and "hang out"?
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