Google's Android division certainly has a sense of humor: It named all of its version codenames after desserts (just as Intel names all of its CPUs after rivers). To celebrate a new version, a giant mock-up of the dessert that matches the codename is usually delivered to the Google Campus and put on display.
So what are the different versions of Android OS and the desserts associated with them? Let us go over a short history.
Android 1.0 and 1.1: Unnamed
There appears to be no codename assigned to versions 1.0 and 1.1 of Android OS.
Google bought a company called Android back in July 2005. Android was headed by several mobile big shots, including the former head of a big carrier, ex-owner of a phone maker, and more. After their buyout, Android went into stealth mode, and rumors spread that Google was working on a mobile phone.
The dam finally broke in November 2007, when Google suddenly announced that they were indeed working on a phone (Google Phone). More than that, they were also working on a brand-new mobile operating system called Android, based on the Linux kernel, to be used by the Open Handset Alliance, a group of 65 different hardware makers, carriers, and other mobile-related companies.
HTC was the first phone maker to get a real consumer phone out, the T-Mobile G1 (also known as the HTC Dream outside of US), on October 2008.
An update of Android, version 1.1, was released in February 2009. However, the first significant version of Android OS that really showcased the power of the platform was V1.5, codenamed "Cupcake."
As Cupcake starts with letter "C", many have suspected that 1.0 had a codename starting with "A" and 1.1 had one starting with "B," but no actual codenames were ever assigned.
What Is AOSP ROM vs. Factory ROM?
AOSP, or Android Open Source Project, is the source of all actual Android code that is open source. While Google did develop and is still developing Android, it periodically releases bug fixes and new versions to AOSP to continue its development. However, AOSP versions of ROM are a very generic ROM and need to be customized for different hardware implementations. You can't just download AOSP stuff into your device and expect it to run.
Thus, many ROM developers take AOSP code, customize it to their purposes, specialize it for one platform/device, and voilà, AOSP-based ROM. Not all features may be supported by AOSP ROM as some hardware does not have open source support.
A factory ROM, on the other hand, is based on the original firmware from the manufacturer. It is basically a tweaked version of the original ROM, probably with bloatware stripped out and tuned for maximum performance. This is only possible if the manufacturer has actually released such a ROM.
For example, to get Jelly Bean on an older phone, such as Motorola Droid Bionic (aka Targa), one can take the official Motorola 4.1 Jelly Bean update, then load one of the tweaked ROMs based on it. Or one can just Cyanogen Mod 10.1, which is based on AOSP. CM10.1 doesn't have nav dock or lap dock support, as those are proprietary to Motorola with no open source support, but it has variety of other features not available on the factory or tweaked ROMs.
