nirodha vs nibbana?

I came across this excellent discussion of nirodha recently: https://buddhism.stackexchange.com/q/3116/2493 wherein nirodha was defined to be "the cessation of suffering" i.e. "the third noble truth". I tend to use the word "nibbana" to represent this phenomenon, so I am a little bit confused about the need for 2 different terms here. If one were to set aside the concept of physical rebirth after death, would any difference between the concepts of "nirodha" and "nibbana" remain? If so, what is the nature of this difference?