Boot Camp External Drive only booting to one computer

The general rule is that the 2015 and newer Macs can no longer boot operating systems using the BIOS method. This is the method used in the installation instructions you refer to. Also, generally 2011 and older Macs can not boot Windows from external drives. Therefore, the installation method, you refer to, generally only works for the 2012 through 2014 model year Mac computers.

The steps to determine if your Mac can BIOS boot operation systems is given below.

1. From the menu bar, select "About this Mac". The pop up window should display the model year and screen size of your Mac. The pop up window for my Mac is shown below. I have a 20-inch, Mid 2007 iMac.

   

2. Goto the Apple web site: Install Windows 7 and earlier on your Mac using Boot Camp. If the "Boot Camp Support Software" is listed for your model Mac, then your Mac can BIOS boot operating systems.

But even if both computers qualify to BIOS boot Windows from external drives, you have the problem of the drivers. One of the steps, in the instruction you refer to, is to install the Boot Camp Support Software. This software installs the correct drives for your model Mac. If you then try to boot Windows using a different model Mac, the installed drivers will be wrong for the this Mac.

You could try installing Windows 10 in EFI boot mode using following steps.

1. Make EFI bootable USB installer

   • Download Win10 install ISO
   • Boot into Windows DVD setup to access a Windows command prompt, or use Windowsd machine
   • open command prompt at install screen by pressing shift+F10, or run cmd

   • load diskpart and make clean install disk by typing:

     diskpart
     list disk
     select disk n #n=USB stick
     clean
     convert gpt
     create partition primary
     format fs=fat32 label=Winstall quick
     exit
     exit
     

   • mount downloaded install ISO

   • drag everything from the mounted ISO onto the USB stick
   • delete bootmgr and bootmgr.efi from the stick to avoid BIOS/CMI boot and force EFI boot

2. Format external HDD to GUID Partition Table

   • Boot into Windows Setup using DVD, or use Windows machine
   • press shift+F10 at install screen, or run cmd

   • load diskpart to convert external drive to GPT:

     diskpart
     list disk
     select disk n #n=External HDD
     clean
     convert gpt
     exit
     exit
     

3. Setup Windows with EFI Boot

   • remove ALL physical drives except the to be Windows drive (if possible)
   • plug in Winstall USB Stick
   • Boot Mac holding option/alt key
   • Choose EFI Boot
   • Enter setup and select external GPT target disk
   • Install Windows 10
4. Install Bootcamp Drivers (optional)
   • Boot into Windows
   • Download Bootcamp Support Software
   • Run Setup

Step 4 might become problematic because every Mac uses somewhat different drivers. Every time you switch to another mac, you'd have to re-install the right drivers using the correct Bootcamp Support software. Otherwise you might loose functionality such as trackpad, volumekeys etc.