http://www.commodoreusa.net/CUSA_AMIGAmini.aspx
What the hell is this?
Amiga, Inc. actually makes new, modern Amigas (boing ball and all) but this looks like some pirate knock-off by a grey-market manufacturer. I'm not even sure how they're getting away with it, considering Amiga, Inc. owns the Amiga brand.
Err... Not quite... "Amiga Inc" is more or less a patent/licensing house. At first they were geared towards an "AmigaAnywhere" run-everywhere OS which didn't quite go anywhere.
In the mordern "Amiga's":
There is an "AmigaOne" series of PPC-based computers that run Amiga OS4 developed (at least principally by Hyperion). The computers themselves: AmigaOne XE/SE and Micro A1 by Eyetech (discontinued), SAM line of computers by Acube and the AmigaOne X1000 by A-EON.
Amiga OS4 can also run on a Pegasos II (more on that later.
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Alternatively, AmigaForever is a version of UAE packaged with other utilities made by Cloanto that have officially licensed Amiga roms.
Commodore USA bought the commodore licence and I think bought licensing to use the Amiga name for another line of PC based computers running its own OS?
Of course there is also MorphOS which is another "Amiga compatible" OS. It's not compatible with OS4 (although there is an library you can install that will give you partial compatibility with OS4) but it will work with software developed for OS3.1 and earlier provided it doesn't do any hardware banging.
MorphOS runs on Pegasos Line of computers (Peg 1, and 2 are both discontinued), Efika PPC (discontinued) and the team is now concentrating on making the OS compatible with PPC-based macs (PowerMac G4's are more or less all compatible, even partial compatibility with the PPC Cube).
Last but not least, there's AROS and its variants. AROS started out as an open-sourced reimplementation of AmigaOS 3.1 (other variants are aiming to add more modern features even if it breaks source-compatiblity). AROS is typically aimed at x86-based systems but could be compiled for 68k and ran on original Amiga Hardware instead of AmigaOS. The good thing is that 68K AROS (and a compiled AROS "ROM") could subtitute AmigaOS in an UAE installation and be used legally.
Of course, to be honest the order of this would be: AROS and MorphOS started their development, then Amiga OS4 followed by Commodore USA's OS.