hangout and hangover are both used in a different scenario.
Hangout
Hangout is a general term used by people when they plan to meet at a common place with their friends, colleagues, family members, anyone. As you may have seen people saying “lets hangout today”, “let's hang out on Sunday”. In general, it means spending time with someone or a group of people in a casual way.
Hangover
it is basically a stage of a human body after heavy consumption of alcohol. This usually happens once the intoxication starts to wear off and is completed being absorbed by the system. Evacuation is symptoms that surface once an individual that's dependent on alcohol or different substances shortstop taking the actual substance.
Drinking has become one of the favorite pastimes in today’s society. Virtually every occasion needs an individual to consume alcohol, at times of happiness, sadness, excitement, sickness, etc. After the consumption of heavy alcohol the next morning a person experiences dullness, headache or any kind of sickness that’s what hangover is all about.