For me post-punk always boiled down to anything that happened after the first wave of punk but somehow, sometimes loosely, still associated with it. So yeah, it is a continuous process. The term really doesn't mean much of anything, as it's often thrown at bands that don't associate themselves much with punk rock or anything that happened before it. Journalists, critics, almost always (naturally...it's almost unavoidable) have this need to compare anything in the now to whatever happened before it. Most find it difficult to describe Jimi without mentioning many of the blues artists that came before him (Buddy Guy, especially) even though, minor similarities aside, have different approaches to music. It works the same way in punk rock or virtually any other genre of music (I honestly don't even consider "punk" a genre these days...it's just rock to me. I guess it could be argued that it's a sub genre of rock...but The Pistols are easily comparable to Chuck Berry, again, even though the two were at the same time wildly different). In other words, it's something that doesn't really mean much of anything.
Were The Velvet Underground really proto-punk? Reality is, your first wave of punk musicians didn't seem to be inspired by them much...but, haha, a lot of their influence can be heard via a lot of "post-punk" bands.
Sonic Youth + Butthole Surfers can easily be described as "post-punk". So can Depeche Mode and New Order. It's all meaningless.
I realize ya still have bands that refer to themselves as punk. I don't think there is anything wrong with this at all...but basically none of them are or ever really were the bands that spring to my mind when I think "punk". I mean, technically Choking Victim and Nausea and all the stupid political crusty shit never really qualified as punk rock at all to me. Punk rock didn't originate as some political movement...people just had to add that nauseating twist to something was just fine without it. To others, it's the only thing that qualifies and the Ramones/Dead Boys..and I DESPISE when people say this..were nothing more than "just rock n roll bands". Most aren't too brushed up on their history either. Same kinda morons that will refer to The Stooges as "hippies". It's just whatever.
Yeah, punk and politics, for me, has always been such a silly concept. It's not much different than when the racists begin associating themselves with skinheads...all but changing everyone's perception of something that initally had NO racist intentions (history teaches us the original skins were really into ska and reggae...you know, traditionally "black" forms of music).
It's nearly impossible in some circles to discuss punk rock as an approach to music, or a historical concept, without someone feeling a need to throw in some political agenda. I always dug The Ramones and Johnny Thunders because they were NOT preachy...I hate Minor Threat and Fugazi solely because they are. Very few bands can get away with that sort of stuff...I feel very few should. A bunch of angry dudes screamin' preachy stuff into a microphone to other angry (and also typically preachy) folks in an audience never changed much of anything.