I've seen both of these words used on television programs, but as far as I can tell they both mean "level"/"steps". Is the word order interchangeable here or do they mean different things?
A search of Wikipedia reveals that 階段 usually means "staircase", but I don't understand why the swapped words have similar but subtly different meanings.
階段 always means staircase. It can be used metaphorically, e.g. 大人の階段を昇る but never to the concept of incremental steps. 段階 on the other hand is never used to refer to staircase and instead refers to the concept of incremental steps/phases, e.g. 段階を経ましょう, 第一段階にある. So they are clearly different. I suppose it was just a convenient way to generate words!
