One of the differences is that when you hang out with your friends, you might be in your own home and never go out.  This would be the case when your friends come over to your house.

Where I am from, we often use the phrase ¨hanging out with ......¨ for times when we are socializing but do not really have an event or activity planned ahead of time (as opposed to a plan to go to a movie, a concert, a sporting event, etc.) 

Hi Yo C,

When we "go out", we are heading out of our residence or a building which we are in at the moment.

Example: Let's go out and do some shopping. / We went out to the beach. 

When we "hang out", we are referring to being in a place where we visit frequently with friends. 

Example: Let's hang out tonight and grab a beer!

We also use "hang out" to refer to (1) something that is protruding. (Example: Your shirt is hanging out. Tuck it in) / (2) hanging of clothes from a clothes line to dry. (Example: The Sun is out! Hang out your clothes to dry.)

Hope this helps.

Cheers, Lance

Are there any differences between GO OUT and HANG OUT??? Thank you!