General Discussion

The rule is that the essential employee is to show up for work but cannot be paid until Congress authorizes the budget their salaries come from. If they want to call in sick, it's supposed to count against their sick leave.

The non-essential employees don't show up for work; they are furloughed.

In both cases, however, they are "made whole" in that when the appropriations happen they are to be paid all their back pay. The essential workers, though, for being essential are still to go to work, with any expense that entails, and cannot get another job because, well, they're full-time employees and that puts a crimp in their availability. Meanwhile, the non-essential employees can stay home (granted, without pay) or get part-time/temp gig if they can find one.