That Debian description is mostly wrong, and there's little reason to think of "Pepper Flash" as being its own thing. It's simply a build of Adobe Flash Player that embeds into browsers using PPAPI (Pepper) rather than NPAPI (Netscape plugin API), because NPAPI support has been discontinued for years by both Google and Adobe. On Windows you will get one of three different versions of Flash depending on browser (PPAPI for Chrome, NPAPI for Firefox, ActiveX for IE), but that's a detail that hardly anyone has to worry about; you don't see a lot of questions about "ActiveX Flash" in particular.
The PPAPI version of Flash is bundled with Chrome and so normally doesn't need to be distributed separately, but Debian includes Chromium, which doesn't bundle Flash, but still supports it, so they need a package to add that in. It's a separate package from the old (NPAPI) Flash plugin because that one is still getting security updates, but it's a completely different version — Flash 11 for NPAPI, and Flash 22 (currently) for PPAPI. Since they update separately and have different versions, they're separate packages, thus "pepperflashplugin" vs "flashplugin". I would have gone for "flashplugin-ppapi" myself, but what can you do?
I believe the reason Debian says Pepper Flash is "maintained by Google" is because Google is the distribution channel for the version of the plugin that they install. And Google probably does do a good chunk of testing on it. But it's definitively not a separate Google product.