The x64 term never really sat well with me. I prefer the bsd method and call it amd64.
i386 intel's 386 architecture
ia64 intel's 64 bit architecture(aka the itanium)
amd64 amd's 64 bit architecture(aka the 64 bit extensions to i386 aka x86-64 aka x64)
It definitely reminds me more of "x86-64", the name used on early publications before they decided to brand it (AMD64, Intel calling it EM64T or something, and eventually x64 appearing as a shorthand). You've got the "86" and a 6, and unlike i386 or i486, "686" never had significant currency as a "real" chip name.
I feel like "i586" and "i686" are sort of a hairball logistically. I can recall a friend in the late 1990s whose forum signature boasted having a "686" overclocked to 262MHz-- an AMD K6. While we sort of understand i586 to mean Pentium, and i686 to be PPro/PII/PIII and beyond, you can make cases for the non-Intel Pentium-class CPUs to be anywhere from i386 (NexGen Nx586-- where's the FPU),to i686 (something like a K6-IiI+ is clearly more advanced than, say, the original i586 Pentium 60, although not necessarily matching PPro additions one-for-one)
Going completely on a further tangent, it feels like we stopped awarding architecture tiers like that. There were definitely new instructions in some of the later-generation parts, why didn't the Pentium III with SSE, for example, become an 'i786' tier? Why is there only one 'amd64'? Guessing the overall strategy is that modern code feature-detects and compilers build a binary with multiple code paths-- something that will run grudgingly on a Pentium Pro or original Socket 940 Opteron, but will pick more efficient code paths on a more recent CPU. Although, wasn't that sort of the promise of things like Gentoo-- by building things yourself, you could make a hyper-lean system knowing it only needed to run on the exact hardware you had? I'd expect a marginal performance uptick, just because you'd be avoiding checks and branches related to feature selection and smaller binary sizes, but it doesn't seem like there's a clear consensus it carries its weight.
