There are many questions about what each genre means, so I would like to write down my views about what those differences are between each genre.
New Wave / Power Pop
New Wave has its roots on Punk Rock, and many Punk Rock bands followed a New Wave direction later. Actually, New Wave is a very generic term, and originally it meant “New Wave of Rock”. Power Pop on the other hand is more based on the Garage Rock movement. But Punk Rock itself is based on the Garage Rock as well. What is also common here is, that both genres are not Blues influenced. The main difference I believe is, that Power Pop songs are supposed to be upbeat songs and their main characteristics are catchy choruses and loud drums. Also Power Pop should include some guitar solos, yet not lengthy ones. Ultimately, drums are supposed to be highlighted in Power Pop. In New Wave on the other hand, guitar solos were supposed to be stripped down, and guitars should be put on the background as a secondary instrument. In New Wave the main instrument is bass. Keyboards are optional in both genres, but if they start dominating the instrumentation then they will lean towards a more Synth-Pop (or Synth-Rock maybe) direction. A Power Pop album would be Whatever Happened To Fun by Candy. Although they were also labelled as Glam Metal because of their image, they were far from that. The songs had also some vibe of 60s, which was also another Power Pop characteristic. Kids In The City, would be the most characteristic song from the genre here. Phantoms by The Fixx on the other hand, was more New Wave, featuring in general a darker sound, instead of the upbeat Power Pop sound. Less Cities, More Moving People would be one of the most characteristic songs of the genre, featuring this punchy bassline all throughout the song.
New Wave / Synth-Pop
Another thing I notice is that every Synth-Pop band is marketed as New Wave too. Although it might be true, because Synth-Pop is based on New Wave basslines, Synth-Pop doesn’t mean it’s New Wave. Synth-Pop (as the name suggests too), is based on electronic instruments. It’s OK if they use some guitar or acoustic drums at certain songs, but electronic instruments are supposed to be the dominant. If for example a song was using keyboards, Drum Machines but the guitar was tuned up, then it wouldn’t be called “Synth-Pop”. New Wave has a more organic sound, and as I said the main instrument there is the bass. Such examples are, Talk Talk's It's My Life and a-ha's Hunting High And Low. The first is New Wave when the latter is Synth-Pop. It's My Life, doesn't use synths as the lead instrument and it gives to the other instruments, air to breathe. Hunting High And Low on the other hand, is based more on electronic instruments.
New Wave / AOR
There are some bands who are labeled as New Wave, but they don’t sound very different than others who are labeled as AOR and vice versa. It’s all about image and vocal range. New Wave artists, were usually dressed in tight shirts and skinny ties. Also the main colors were Black/White/Red and the long Rock ‘n Roll hair were hardly seen in New Wave fashion, but they had longer on the front/shorter on the back (usually including a fringe) hairdos mostly. Make-up was also a common trait among men as well. AOR bands were having a more typical Hard Rock image. Listening to the debut albums of Foreigner (AOR) and The Cars (New Wave), they don’t sound much different, with the exception of vocal ranges. New Wave vocalists tended to have more “geeky” and “distant” voices. By “distant”, I mean they were not singing the song from a typical Rock Star’s point of view, but they were more like “narrating” it. Also the New Wave vocals were more high-pitched. But personally I believe The Cars are Power Pop not so New Wave.
AOR / Power Pop
There are two albums I have in mind, that they have been labeled as both genres. Rick Springfield’s Working Class Dog and Honeymoon Suite’s Self-Titled album. But I would say Rick Springfield’s album is Power Pop and Honeymoon Suite’s is Power Pop for the most part but there were AOR elements and also New Wave elements too. You can hear the pounding drumming sound in songs like Carry Me Away, Love Is Alright Tonite, Everybody’s Girl, etc. Also another notable thing is that songs are shorter length (average running time is about 3 minutes, when most AOR songs tend to last about 4 minutes). There’s another song called Inside Sylvia which is more like a Synth-Pop ballad, so it kinda sticks out as the exception of the rule.
As for Honeymoon Suite, there were AOR songs like New Girl Now and Burning In Love (Those are also the most known songs of the album). Wave Babies was more like a New Wave song and Stay In The Light was Power Pop. The rest of the album is also Power Pop with the exception of Face To Face which is perhaps more like New Wave? Or maybe AOR? Or maybe…Post-Punk? Anyway it’s hard to define this one.
Synth-Pop / AOR
There’s an AOR subgenre called Hi-Tech AOR which is often labeled as Synth-Pop, but it’s not. Take for example the albums Tao by Rick Springfield and Strange Behavior by Animotion, and the two albums by Naked Eyes, Burning Bridges and Fuel For The Fire. Tao and Strange Behavior are Hi-Tech AOR because guitar work is present, especially in Strange Behavior, but still there are Synth-Pop cuts like Celebrate Youth from Tao and I Engineer from Strange Behavior which were pure Synth-Pop (side note: both did very well in Germany, despite coming from non German artists. Seems like Germany was really digging Synth-Pop). Naked Eyes’ albums were Synth-Pop and not Hi-Tech AOR on the other hand, because they were strictly based on electronic instrumentation. You won’t hear any guitars or acoustic drums here. In conclusion Hi-Tech AOR is based on Synth-Pop indeed, but the use of Hard Rock sounding guitars is required to move away from the Synth-Pop realm.
AOR / Glam Metal
Sound-wise the differences are minor actually, especially when it comes to Power Ballads. I believe it’s all about the image. For example, Europe are considered a Glam Metal band and Survivor are considered an AOR band. But if you listen to Europe’s albums The Final Countdown and Out Of This World, and Survivor’s albums Vital Signs and When The Seconds Count, then you will notice that there are almost no differences in terms of sound. So, if Europe didn’t have the trademark big hair and make-up that Glam Metal bands of the era used to have, they might be labeled as an AOR band. Likewise if Survivor had the stereotypical Glam Metal image, then they will be viewed as a Glam Metal band.