Officially, a furlough is not a vacation - at best, it's a stressful stay-cation with an unknown end date.
Per the Office of Personnel Management's official guidance:
2. Will employees who are furloughed get paid?
A. Congress will determine whether furloughed employees receive pay for the furlough
There is no guarantee that employees will get that pay back, and they are certainly not being paid during the shutdown (which presents cash flow issues for them).
That said, every time there has been a shutdown, Congress has ended up authorizing back pay, so it's likely to be true this time too.
So, in some respects, it's similar to a vacation, but there are some important differences:
- You can't leave town or make future daytime plans, because a deal could be reached at any time, and you would need to report to work the next day. (It's unlikely that a deal will be reached and a budget passed while Congress is not in session for the holidays, but if Trump or the Democrats fully gave in, it's likely an emergency session to pass it would be called.)
- You aren't getting your regular paycheck, and your last paycheck will only cover the days that weren't part of the shutdown - this could make paying the mortgage, credit card bills, or even for groceries problematic for employees who are in precarious financial situations. The OPM even has sample letters to send to creditors about making reduced payments.
- Following from both of those is the uncertainty. You'll probably be paid, but you can't be sure until it shows up (or at least until Congress passes a law on the subject). That would put a damper on any enjoyment of the time off.
- There's no one doing your work, but deadlines don't (generally) move. Unlike a vacation, where cowokers can pick up your slack, things just aren't being done. So when you go back, you're going to have to work extra hard to catch up.
All that said, issuing back pay for time spent not working does cost the government significant amounts of money. So working out a resolution involving it is generally a part of whatever budget negotiations are going on. It also acts as increasing pressure on both sides to come to some kind of compromise.