Withholding
Tax an employer deducts from wages and remits to a state on the employee's behalf — an advance payment against a liability, not the liability itself.
Withholding and liability are separate questions, and conflating them causes most of the confusion in this subject. Which state withholds is set by payroll on the basis of the certificates it holds. Which state is owed tax is set by residency and sourcing rules. When those two answers diverge, the difference turns up as a refund from one state and a balance due to another.
Nothing is withheld from a 1099. A contractor holds the money that a W-2 employee never sees, and pays it directly as quarterly estimated payments — which is why an out-of-state client changes nothing about withholding and only ever raises a sourcing question.
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In one sentence
What is withholding?
Tax an employer deducts from wages and remits to a state on the employee's behalf — an advance payment against a liability, not the liability itself.