The English language verbs Get Out and Go Out have related meanings, but they are different, as I shall explain, using British English examples.
To Go Out implies movement from being in to being out. It is used when the destination is more important than the means of getting there. It is normally voluntary.
"Do you want to go out and get a sandwich together?"
"I am going out tonight."
Romantic, unmarried couples are said to be "going out" with each other.
"Tom and Daisy have been going out for three years now."
To Get Out is used when not being inside is the most important thing. It is often critical to do this, not chosen. It is used when you need to imply being released from "being in".
"I need to get out of the house, the kids are driving me crazy."
"Get out, there is a fire!"
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