Confusing architecture naming convention

I just bought a new laptop. It has a 64-bit 2 GHz Intel dual-core processor. I want to install a 64-bit Debian on that laptop. Therefore, I headed to this download page. It showed the following available architectures: alpha, amd64, arm, armel, hppa, i386, ia64, mips, mipsel, powerpc, sparc, s390, source and multi-arch. I'm stocked and confused as I don't know which architecture to download. By deduction, I only have 3 choices: amd64, i386 and ia64. I wasted an hour reading the how-to of the 3 architectures to no avail. I spent another hour searching on the internet and finally stumbled on the Debian wikipedia page that shows the meaning of each architecture. Here is the important part:

i386
x86 architecture designed for Intel/AMD 32-bit PCs. Also compatible but not recommended on Intel/AMD 64-bit single/multi core PCs
amd64
x86-64 architecture designed for Intel/AMD 64-bit single/multi core PCs
ia64
Intel Itanium (IA-64) architecture

Why in hell they are calling x86-64 architecture amd64? The "amd" part is freaking confusing. Obviously, if you have an Intel processor, you wouldn't want to install something that has "amd" in it. You are wondering: Is this "amd64" reserved exclusively to AMD processor only?

To the Debian maintainer, please change amd64 to something generic or at least put the description on the download page so people know what they mean.