The aim of this post
This post aims to be a help for computer newbees, or those who are working in the application layer but somehow have to buy a new server and install Linux on it, but are confused by those complex naming of CPU architectures (i386, x86, IA64, ...).
Note that this post shows which CPU "instruction set" architectures are compatible/different, but it does not step into how each "micro" architectures are different (e.g. Skylake vs Broadwell).
At a glance
If more than 1 name is shown in the "Arch Name" column, you can expect they are all the same. If you're interested in why a single instruction set architecture has several names, you can refer the next section.
|x64, x86_64, AMD64, EM64T, Intel 64||So called "64 bit CPUs". Note that AMD64 (not IA64) is in this group. Software for AMD64 work on your 64 bit CPUs from Intel, but software for IA64 don't. Note also IA64 and Intel 64 are different.||Core i3/5/7, Xeon E3/5/7, Core 2 Duo, Opteron, Phenom, Athlon 64, ...|
|x86, i386, IA32||So called "32 bit CPUs". Normally you never buy a new machine in this group, but old servers might still use it.||Pentium 2/3/4/D *1, Celeron M/D, Athlon *2, Duron, ...|
|IA64||Another 64 bit architecture from Intel, but never became popular. Don't use it unless you're 100% sure what you're doing. IA64 is 0% compatible with x86 or x64.||Itanium, Itanium2|
|Power (IBM)||Currently the only way to use NVLink between the CPU memory and the GPU memory. You might want it if you do deep learning with ~100GB of data. Not sure if it's a good investment as Intel should get NVLink compatibility sooner or later.||Power 7, ...|
|ARM||Currently used only for embedded and mobile devices. Never care them for now if you live in the app layer (might become different in few years though).||Cortex-A9, ...|
|MIPS||Ditto.||don't really know|
*2: Althon is even worse because the original 32 bit version was "Athlon", then 64 bit versions named "Athlon 64" were released, after that AMD removed "64" from later 64 bit versions and they're named just new "Athlon" (like iPad -> iPad3 -> the new iPad).
OK, so why a single instruction set architecture has many names? Here's the history.
They originate from old Intel CPU series: 80386, 80486, 80586, 80686, etc. 80386 was the first 32 bit CPU from Intel, and the successive ones were named 80486, 80586, 80686, ..., so from some point they started to be called x86 (x can refer 3, 4, 5, 6, ...). The instruction set architecture used in 80386 was called i386 ("i" from "i"nstruction), but people refer the architecture (i386) and its implementations (x86) interchangably. i386 is also called IA32, meaning "I"ntel "A"rchitecture with "32" bit addressing.
The reason why (relatively) recent CPUs such as Pentium 4 are also called x86, is that they are still backward compatible with 80386. This means that any instructions supported in 80386 are supported in Pentium 4, which does not necessarily mean any old programs written for old computers work in recent ones. For old software to run on newer machines, they require OS- or compiler- level ABI/API compatibilities. However the compatibilities (especially OS-level ones) are kept very carefully, because for computers to sell the most important thing is if they have lots of applications to go (that's one of the reasons IA64 could not become popular, that's why Windows phones never pop into your choices).
They are extended versions of x86, which can handle 64 bit address spaces (meaning that they can utilize more memory natively) and have other advantages as well. In this meaning they are called x86_64, also x64 for short. A confusing point is x64 is newer than x86 although the number is smaller. You may go crazy if I tell you about x32, which is a concept newer than x64. It's like a mixture (combining good things) of 32 and 64 bit modes, but normally you still don't see it often now.
Now why this is also called AMD64, is that AMD was the first (major) vendor to extend x86 into the 64 bit mode. After that Intel created EM64T, which is compatible to AMD64. This was a big deal because AMD was/is a vendor creating CPUs compatible to Intel architectures, but for this thing AMD was a step ahead of Intel. Today some people say Radeon Instinct, a GPU for deep learning which AMD claims faster than Titan X, is a big deal from AMD after 10 years; the one 10 years ago is this AMD64. :)
Wait, but why didn't Intel name it IA64 instead of EM64T?? That's because at that time IA64 already existed, and it was a brand-new 64 bit architecture that had no compatibility with x86. Intel's first aim was to replace old x86 by IA64 (the actual implementation was named Itanium), but for many reasons it failed. What is really confusing, is after several years Intel gave a new name to EM64T, that is Intel 64!
*3: There are a lot of differences in fact, especially in additional functionalities such as Intel VT or SSE, but that's not the topic of this post.