Wave monsters are those capable of utilizing a mysterious energy called Wave that Energy has it's own second set of attributes though the main attribute on a wave monster is always the wave attribute. Wave HERO monsters are the Elemental HERO monsters of the wave attributes. Unlike regular attributes they may not be limited to 6.
Some examples of Wave Attributes, include, Solar/Sun,Lunar/Moon,Storm, Heart, and Meteor and Comet
Wave monsters are more a super type that can go in anything but those with negative numbers like the canon Dark Synchro they'd also not be able to touch Dark Tuners.
So can only Waves could be wave normal, wave effect, wave ritual,wave/union, wave/spirit, wave/gemini,wave fusion,wave contact fusion, wave tuner, wave synchro of various sorts, wave xyz/cyz/syz, and wave pendulum.
Dark wave is the anti wave energy and used by the fallen Dark Wave HERO. Some examples of it include Void, Blood, Toxic, etc..
Obvious dark wave would use anything in negative levels, so most of that wouldn't be canon.