Mods are not "Modern Day punks" like Green Day or Sum 41.
Mods are in the Punk scene, but not necessarily punks.
See Mod or Mods
> She's a Mod
Modpunk is the modified alternative to punk rock music. Usually consisting of ambient sounds, harmonies, and awkward time structures. Lyrically, it is no longer just in response to politics, but also life issues and love. Such core bands of this genre are the likes of End of Duhline, No Inside, etc.
Bands or artist that have classic punk inspiration, but have come out recently.
Modern Punk Rock.
Mod-Punk: You're right, they're Mod Punk, the next step.