Pepper Flash Player is maintained by Google, and is newer than Adobe Flash Player. Adobe currently still provides security fixes for Adobe Flash Player. Google provides newer features in Pepper Flash Player. Pepper Flash Player can currently only be used with Chromium (and with Chrome).
The package is a separate Debian package, not integrated in flashplugin-nonfree. Users can choose between Adobe Flash Player and Pepper Flash Player by installing the corresponding Debian package. Both packages will co-exist for some time, until Adobe finally ends security support for the Adobe Flash Player. Pepper Flash Player uses a different interface with the browser than Adobe Flash Player, so it doesn't fit in the mechanism of "alternatives" (flash-mozilla.so). When both are installed on one system, then Chromium currently only sees the Pepper Flash Player.
The design of the Debian package for installing Pepper Flash Player is similar to flashplugin-nonfree. The difference is that flashplugin-nonfree downloads just the Adobe Flash Player, while for Pepper Flash Player the Debian package downloads Google Chrome, and then unpacks it to make the included Pepper Flash Player available for use with Chromium. Other than that, the mechanism is the same. A different design would be to simply include the Pepper Flash Player in the Debian package. But the upstream license doesn't allow that. Another design would be to bump the Debian package version for each newer Pepper Flash Player. But that would reopen the debate on how to get the updated Debian package in stable in a user friendly way and sufficiently fast. Note that the Debian package would pull in a combination of feature updates and security fixes in a new upstream release of closed-source software, which is somewhat difficult for Debian procedures to install quickly in stable. So for now I'm sticking to the design of flashplugin-nonfree for the same reasons that package is designed that way.
Since pepperflashplugin-nonfree 1.8.3+nmu1, it downloads Pepper Flash Player plugin from Adobe directly. The following notes are only applied to old versions. Adobe now provides flash (both PPAPI and NPAPI version) at https://get.adobe.com/flashplayer/otherversions/
If installation or update fails with error like this:
ERROR: failed to retrieve status information from google : W: There is no public key available for the following key IDs: 1397BC53640DB551
It happens because google changed it's signing key. To fix it(1):
gpg --keyserver pgp.mit.edu --recv-keys 1397BC53640DB551 gpg --export --armor 1397BC53640DB551 | sudo sh -c 'cat >> /usr/lib/pepperflashplugin-nonfree/pubkey-google.txt'
How to install Pepper Flash Player at PepperFlashPlayer/Installing
Use Pepper Flash with Firefox using Freshplayerplugin