I'll try to explain a little bit of the history of the OS, to help explain the various factions in the Amiga community...
When Commodore was producing Amigas, the Amiga OS that ran on top of them ran from the Amiga OS 1.x series to the Amiga OS 3.x series, with Amiga 3.1 being the last version that was produced before Commodore went bankrupt.
After Commodore went bankrupt, the future of the Amiga was uncertain. Some Amiga users began debating how to take the platform forward. After a lot of debate, this culminated in the decision to start by creating an open-source OS based on the design of Amiga OS 3.1, which could be used as a platform for future improvements. This became the AROS project.
Ownership to the official Amiga assets (OS, patents and hardware) changed hands a number of times. The common pattern seemed to be a purchase by a PC manufacturer, who would then outsource the development of the platform through a dedicated subsidiary. First owners were Escom. Second owners were Gateway. Gateway was purchased by Acer at one point, so I believe the current owners are Acer. However, as mentioned previously, official development of the platform was managed by subcontractors, that went under names like 'Amiga Technologies' and 'Amiga Inc'.
Another OS split would happen because of the lack of new hardware coming from official sources. During the time when the official owners of the Amiga appeared increasingly incapable of bringing new hardware to market, a series of PowerPC accelerators appeared for classic Amigas (classic Amigas are based on the 68k family of processors). At first, these PPC accelerators would run on software designed to work alongside Amiga OS 3.x, but in time this evolved into a dedicated PPC-based OS for Amigas. This became MorphOS.
What about the official developments? So after Amiga OS 3.1 there were two additional releases in the 3.x series, 3.5 and 3.9. IIRC of these releases were developed by a company called H&P (Hauge & Partner, or something like that). At one point, it looked like MorphOS would become AmigaOS 4.0, however a couple of the H&P developers formed a new company called Hyperion and convinced Amiga Inc to let them develop the PPC version of Amiga OS, which became the Amiga 4.x that exists today.
There were various other twists to this tale that I've glossed over, but notable mention should go out to Amithlon (sp?), which was an unofficial AmigaOS port/emulator for x86 hardware. At one point there was some hope that this could've been used to pushed the Amiga forward, but it never got the official backing it needed.
So in terms of the remaining factions, it's arguable that four remain:
1. Classic Amiga (68k-based AmigaOS, running on either real or emulated hardware).
2. AROS.
3. AmigaOS 4.x.
4. MorphOS.
In terms of software releases, there's still a small amount of new releases, but killer apps that would be worth investing in the platform for are thin on the ground. Closest to that you'll probably find is Hollywood, but it's available for non-Amiga platforms now too:
http://www.hollywood-mal.com/