As mentioned before the various tags applied to a range of music back then do get a bit confusing. At times punk bands, or those who emerged shortly afterwards, were referred to as New Wave. That tag is perhaps most commonly applied to a further style of music that emerged in the late 1970s and early 1980s.
Even then many definitions conflict. Elapsed time and different memories have seen some bands cross over among the categories. There is also a definite new wave overlap with punk, pub rock, synth-pop, new romantics, and others.
What counts as a song from a new wave band?
The lines for where many bands fit are very blurred. Elvis Costello And The Attractions, for example, are classed in some lists as pub rock, in others as post-punk, and here and there as new wave. Duran Duran is referenced as New Wave at times but also included as new romantics alongside Spandau Ballet. Blondie is another huge band that seems to fit into more than one of those categories.
New Wave definitely takes its lead from punk and the bands that followed, but often adds in something more than raw, fast, and aggressive guitar. That extra varies but includes one or more of keyboards and synthesisers, a quirky style or unusual lyrics, or some gothic elements, while others bring an arty background and style. There are plenty more possible elements to be added, which doesn't help at all in seeking a definition.
What follows is my list of three great records from top new wave bands. As with the examples for punk and post-punk, there will be differing views on selecting the three songs to include. There's also the debate on whether these are from truly new wave bands, they are in my mind but come from quite different parts and times within that category.