That's funny, because it amounts to the same thing really 下岗. Actually, a person is fired "for cause", which means committing some infraction (sleeping on the job, impregnating the boss's daughter). Being laid off is to be "made redundant", a euphemism (of which there are many).

They are different. Someone is usually fired for misconduct. Even a good worker's job can be replaced by a new machine. In that case, he is said to be redundant (the purpose he served is already being done by something/someone else). For words with which you are not familiar, you can always look them up on Wikipedia, the online dictionary.

The key word here is "euphemism".