No. I think it is not like that.
"hang up" is a phrasal verb. "hang out" is a different phrasal verb.
The combination takes on a whole new meaning that will not be the same for another verb & "up" or "out" combination.
"hang up"- verb means to finish a telephone conversation. eg "end" on the cellphone.
He was rude, so I hung up.
Also: A hang up "hangup" "hang-up" (noun) can be something you have an issue over.
She has a hang up about cats. Don't talk about cats when she's round.
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"hang out" is to be relax, be lazy somewhere.
It is only early. I'm going to Sara's place to hang out for a while.
I'm going to hang out at the mall for a while.
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"hang out" can also be a noun. Her favourite hang out is starbucks. This one is often "hang-out" or "hangout".
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To illustrate "tie" is a verb, "tie up" is another verb.