Just as the title reads i can't quite understand how it works flawlessly. From what i know the 32bit OS works on both 32bit & 64bit processors but 64bit OS only work on 64bit. So how is it possible that it works? I also noticed, when downloading the ISO, from the Ubuntu site that the 64bit version had some 'amd64' along its name and the 32bit version 'i386'. Does the 'i' stand for Intel?
Short answer: Your laptops have 64bit CPUs.
When we talk about 64bit, we're talking about
To translate this out of Geekish, 64bit CPUs can run everything a 32bit CPU can. I suspect this is what has happened to you and this is where the confusion has arisen. I suspect you had 32bit operating systems installed on the laptops before. A 64bit CPU is more than capable of doing this.
But 32bit CPUs cannot run 64bit code. They have neither the vocabulary or the capacity to run 64bit-compiled commands.
So in order for your laptops to run
The i does indeed stand for Intel and the 386 stands for the Intel 80386 CPU which is long obsolete. This label refers to the instruction set that Intel used for its 386, and beyond, line of CPUs. AMD designed their own CPUs to run that Intel 386 instruction set. Which is why the Windows and Linux operating systems run on both Intel and AMD CPUs. We do not need a special version for Intel and AMD.
One the other hand, AMD was first to develop the i386 instruction set to fully exploit the capabilities of 64bit CPUs with Intel having to follow AMD's lead. This is why one of the designations of a 64bit OS is amd64. It does not mean that we need a version of the OS for AMD CPUs and another one for Intel CPUs.
It also explains why a 32bit OS will run on 64bit AMD and Intel CPUs. The 64bit OS is a development of the 32bit OS and backwards compatibility was designed in. It most definitely should not work the other way around.
First of all, to have a 32-bit only AMD laptop, it would have to be with Athlon XP-M CPU, which would mean that it'd have to be 6-9 years old. Any newer Athlon mobile CPUs, like for example Turion were 64-bit (which are backwards compatible with 32-bit, so they can run both 64- and 32-bit code).
i386 means Intel architecture, also known as x86. It's a 32-bit architecture.
amd64 means 64-bit extension of x86 architecture, it was originally created by AMD. It was previously known as x86-64, but later AMD64 and Intel 64 diverged a bit and AMD renamed it. Intel still uses name x86-64.
The most plausive case is that you didn't know, but your computer support 64-bit architecture, to see if it's true type in the terminal:
Then see the "flags" output, if there is one entry named