You have X months notice ie the company has to tell you X months before yoir severance date.
Often the company will want somone they let go out of the office ASAP.
Thus you spend your X months on gardening leave paid as normal wages.
On your severance date you get your redundancy package - in the UK there is a defined minimum but in some markets e.g. finance they pay more as they do want to keep current employees happy so they see that they just don't get thrown out.
As much of the US is at will employment I doubt this scenario will occur often
It can happen during a partial acquisition where the relevant employees are likely to cause damage to or steal the product/property before the acquiring company has finished the acquisition (e.g. software with wide access that needs to be untangled).
The usual one I hear about is someone who’s in generally in good standing and who has a significant stock award coming, but who just isn’t “working out” and management gives them the gift of finishing out their term to get the bonus
