Short answer: Your laptops have 64bit CPUs.

When we talk about 64bit, we're talking about x86-64. This is an extension to i686 developed by AMD. They since went on to rename it to amd64 and since then a billion more names (including: x64, IA-32e and Intel 64) have come into being... But they all mean the same thing. (Sidebar: IA-64 is completely different and has very little to do with x86)

To repeat: x86-64 is an extension. It has all the CPU registers that an i686 CPU has, but with extra ones. An i686 CPU has all those of an i586 CPU, with extras. The same repeats down to i386. The purpose of this "super-setting" of registers/instructions is to keep things completely backwards compatible.

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 x86-64-compiled software, they need to be x86-64 CPUs. It just wouldn't work otherwise.

If you disagree, edit your question to include the make and model of the laptops, and I'll confirm the hardware specs...

And i386 stands for "Intel 80386", as you guessed.