Among music writers, terms get thrown around sometimes without full consideration of what they mean or why they mean what they do. This is probably a relatively common problem for post-punk, the sweeping, generalized form of '80s early alternative rock that can be overwhelming to grasp upon first glance. However, the simplest and most precise way to summarize this form, I think, is to focus first on the name, which suggests music that followed the punk rock explosion of the mid-'70s in America and 1977, more famously, in England. But like any creative movement, it takes time for the bread to rise.
That, of course, is where the '80s come in. To be sure, there was certainly some '70s music that qualifies as post-punk both on a timeline as well as in terms of the second, more important part of the genre's definition: generally experimental, strange and challenging interpretation of the basic aggressive three-chord anger of punk. Therefore, while the Knack were a little punky, that band was always essentially a pop band working strictly within such orderly conventions. On the other hand, bands like Gang of Four, Wire and Magazine took the basic punk template onto fresh paths as the new decade began.
The Golden Years of Post-Punk:
Amidst the popular early-'80s genres of new wave and synth pop (which seldom if ever overlap with the form on which we're focused), post-punk truly exploded during the first half of the decade. As bands moved further away from imitating or repeating the Sex Pistols or Ramones sound, a choice often thrust itself upon early-'80s artists of this ilk: go pop (new wave), take punk rock even further in its purest form (hardcore), or use the music as a palette for experimentation, the exploration of various musical and lyrical complexities and arty daring (post-punk). Luckily, many took that third choice.
Further Differentiation From College Rock & Indie Sounds:
While post-punk music certainly fit into the college rock or indie files of the early '80s, it's actually far more specific than either of those forms. For example, the gloomy, romantic dirges of Nick Cave, the psychobilly buzz of the Cramps, and the dreamy, provocative weirdness of the Soft Boys seem to me far more squarely in the post-punk camp than the more straightforwardly accessible work of Simple Minds, Adam Ant or even U2. All of these groups share post-punk elements, to be sure, but the immediately jarring, unprecedented nature of, say, the Violent Femmes' music raises a post-punk flag more than any other.
The Ultimate Subjectivity of Post-Punk:
So now that we have all that straightened out... Actually, the many perspectives of music fans either render this kind of careful categorization completely moot or turn it into a fascinating exercise, depending on one's approach. Still, as a rule of thumb, the more angular, jagged, complex, esoteric and unselfconsciously quirky the music, the more likely it stands up to scrutiny as classic post-punk. As yet another example, I'm listening to the Smithereens right now, a guitar pop band and college rock act for certain but only marginally post-punk at best, due mostly to the group's exquisite hooks.