Question: how many designs re there for the computer that runs on the RISC-based PowerPC G4 processor, designed by the AIM development alliance and initially produced by Motorola, and preceded by the first laptop to use the PowerPC G3 ?

Context paragraphs:
PowerPC 600: The PowerPC 600 family was the first family of PowerPC processors built.  They were designed at the Somerset facility in Austin, Texas, jointly funded and staffed by engineers from IBM and Motorola as a part of the AIM alliance.  Somerset was opened in 1992 and its goal was to make the first PowerPC processor and then keep designing general purpose PowerPC processors for personal computers.  The first incarnation became the PowerPC 601 in 1993, and the second generation soon followed with the PowerPC 603, PowerPC 604 and the 64-bit PowerPC 620.

Xserve: Xserve was a line of rack unit computers designed by Apple Inc. for use as servers.  When the Xserve was introduced in 2002, it was Apple's first designated server hardware design since the Apple Network Server in 1996.  In the meantime, ordinary Power Macintosh G3 and G4 models were rebranded as Macintosh Server G3 and Macintosh Server G4 with some alterations to the hardware, such as added Gigabit Ethernet cards, UltraWide SCSI cards, extra large and fast hard drives etc. and shipped with Mac OS X Server software.  The Xserve initially featured one or two PowerPC G4 processors, but was later switched over to the then new PowerPC G5, transitioned to Intel with the Core 2 based Xeon offerings and subsequently switched again to two quad-core Intel Nehalem microprocessors.

List of PowerPC processors: 32-bit and 64-bit PowerPC processors have been a favorite of embedded computer designers.  To keep costs low on high-volume competitive products, the CPU core is usually bundled into a system-on-chip (SOC) integrated circuit.  SOCs contain the processor core, cache and the processor's local data on-chip, along with clocking, timers, memory (SDRAM), peripheral (network, serial I/O), and bus (PCI, PCI-X, ROM/Flash bus, I2C) controllers.  IBM also offers an open bus architecture (called CoreConnect) to facilitate connection of the processor core to memory and peripherals in a SOC design.  IBM and Motorola have competed along parallel development lines in overlapping markets.  A later development was the Book E PowerPC Specification, implemented by both IBM and Freescale Semiconductor, which defines embedded extensions to the PowerPC programming model.

PowerBook G4: The PowerBook G4 is a series of notebook computers manufactured, marketed, and sold by Apple Computer, Inc. between 2001 and 2006 as part of its PowerBook line of notebooks.  The PowerBook G4 runs on the RISC-based PowerPC G4 processor, designed by the AIM (Apple Inc./IBM/Motorola) development alliance and initially produced by Motorola.  It was built later by Freescale, after Motorola spun off its semiconductor business under that name in 2004.  The PowerBook G4 has two different designs: one enclosed in a titanium body with a translucent black keyboard and a 15-inch screen; and another in an aluminum body with an aluminum-colored keyboard, in 12-inch, 15-inch, and 17-inch sizes.

PowerPC 7xx: The PowerPC 7xx is a family of third generation 32-bit PowerPC microprocessors designed and manufactured by IBM and Motorola (now Freescale Semiconductor).  This family is called the PowerPC G3 by its well-known customer Apple Inc., which introduced it on November 10, 1997.  The term "PowerPC G3" is often, and incorrectly, imagined to be a microprocessor when in fact a number of microprocessors from different vendors have been used.  Such designations were applied to Macintosh computers such as the PowerBook G3, the multicolored iMacs, iBooks and several desktops, including both the Beige and Blue and White Power Macintosh G3s.  The low power requirements and small size made the processors ideal for laptops and the name lived out its last days at Apple in the iBook.

Macintosh Processor Upgrade Card: The generically named Macintosh Processor Upgrade Card is a central processing unit upgrade card sold by Apple Computer, designed for many Motorola 68040-powered LC and Performa model Macintoshes.  The card contains a PowerPC 601 CPU and plugs into the 68040 CPU socket of the upgraded machine.  The Processor upgrade card required the original CPU be plugged back into the card itself, and gave the machine the ability to run in its original 68040 configuration, or through the use of a software configuration utility allowed booting as a PowerPC 601 computer running at twice the original speed in MHz (50 MHz or 66 MHz) with 32 KB of L1 Cache, 256 KB of L2 Cache and a PowerPC Floating Point Unit available to software.  The Macintosh Processor Upgrade requires and shipped with System 7.5.

CherryOS: CherryOS was a PowerPC G4 processor emulator for x86 Microsoft Windows platforms, which allowed various Apple Inc. programs to be operated on Windows XP.  Announced and made available for pre-orders on October 12, 2004, it was developed by Maui X-Stream (MXS), a startup company based in Lahaina, Hawaii and a subsidiary of Paradise Television.  The program encountered a number of launch difficulties its first year, including a poorly-reviewed soft launch in October 2004, wherein "Wired Magazine" argued that CherryOS used code grafted directly from PearPC, an older open source emulator.  Lead developer Arben Kryeziu subsequently stated that PearPC had provided the inspiration for CherryOS, but "not the work, not the architecture.  With their architecture I'd never get the speed."

Power Macintosh G3: The Power Macintosh G3 (also sold with additional software as the Macintosh Server G3) is a series of personal computers designed, manufactured, and sold by Apple Computer Inc. from November 1997 to August 1999.  It was the first desktop Macintosh to use the PowerPC G3 microprocessor, and replaced a number of earlier Power Macintosh models, in particular the 7300, 8600 and 9600.  The introduction of the Desktop and Mini Tower models coincided with Apple starting to sell build-to-order Macs directly from its web site in an online store, which was unusual for the time as Dell was the only major computer manufacturer doing this.  Apple's move to build-to-order sales of the Power Macintosh G3 also coincided with the acquisition of Power Computing Corporation, which had been providing telephone sales of Macintosh clones for more than two years.

PowerBook G3: The PowerBook G3 is a series of laptop Macintosh personal computers designed, manufactured and sold by Apple Computer from 1997 to 2001.  It was the first laptop to use the PowerPC G3 (PPC740/750) series of microprocessors, and was marketed as the fastest laptop in the world for its entire production run.  The PowerBook G3 was succeeded by the PowerBook G4.

PowerPC G4: PowerPC G4 is a designation used by Apple Computer and Eyetech to describe a "fourth generation" of 32-bit PowerPC microprocessors. Apple has applied this name to various (though closely related) processor models from Freescale, a former part of Motorola.  Motorola and Freescale's proper name of this family of processors is PowerPC 74xx.

Supporting paragraphs: PowerBook G3 PowerBook G4
Answer: two different designs