It’s better known as the payroll tax cut… probably so it can be portrayed as helping the little guy…the employee. Short-term help sure; long-term not so much.
However it also applies to self-employed individuals who pay a self-employment tax on their annual Form 1040 each year… somethng that has nothing to do with payroll.
I seem to recall that social security funding that is reduced by the cut is made up by transfers from the general fund…but I can’t find anything specific on that.