A layoff is permanent, and even if the position is reinstated, you have no claim to get your old job back. A furlough is meant to be temporary and some benefit

A layoff is permanent, and even if the position is reinstated, you have no claim to get your old job back. A furlough is meant to be temporary and some benefits may contain to be paid out. If the company starts bringing people back in, those on furlough will be rehired first if still available. That said, if the company doesn't recover fast enough or goes under entirely, there's no difference in practice.