Many people might use the synonymously. But not all. New Wave would be considered more accessible or pop related. Post Punk was more Avant-Garde and dissonant, including No Wave.
So the Police would be post-punk then New Wave (or at the same time) then pop/rock?
Also, during the late 70s and very early 80's I never remember anyone using the post-punk or alternative label. This was created by music critics much later. It seemed to me that the description of "Alternative Music" came about around when MTV's 120 minutes was on the air for some time - say until the very late 80s early 90s. From my recollection.