Adobe is just the company that made that one type of DRM (they also created the PDF format).
"Adobe Digital Editions" is one particular type of DRM - it's often shortened to just "ADE" around here. It allows you to have 6 computers and 6 other devices (eReaders) registered, and you can view your eBook on any of those devices. You'll need the software called Adobe Digital Editions installed on your computer to get your downloads. You can find it
here. ADE DRM can exist on both PDF and EPUB files.
eReader DRM is different -- rather than restricting the number of devices you can read your eBook on, it encrypts the book using your name and credit card number, which you must enter to read it. The idea here is that you won't want to give away your card number to friends, and so you won't give them the book. eReader DRM can exist on PDB format files.
Mobipocket is another form of DRM, which I'm not too familiar with. Kindle uses its own variant of Mobipocket DRM. Mobipocket formats are PRC and MOBI.
Jetbook-lite can handle eReader DRM (PDB). Libre can handle ADE DRM (PDF and ePub).
Full list of Libre-supported formats:
PDF (Adobe Digital Edition DRM/non-DRM), TXT, FB2, EPUB (Adobe Digital Edition DRM/non-DRM), MOBI (non-DRM only), PRC (non-DRM only)and RTF electronic book format