"aarch64" and "arm64" are the same thing. AArch64 is the official name for the 64-bit ARM architecture, but some people prefer to call it "ARM64" as a continuation of 32-bit ARM.

On the other hand, all 32-bit versions of ARM were called "arm"-something (there is no such thing as "aarch32"). See this other post and this one about the meaning of "armhf".

One of these names is very different – "amd64" is the original name for x86_64, which is the 64-bit version of the usual Intel/AMD x86 CPU architecture found on typical PCs and has nothing to do with ARM CPUs. (The 32-bit version originates from Intel and is always called "x86" or sometimes "i386", "i686", but never "amd32". Only the 64-bit extensions were created by AMD.)

Your Raspberry Pi 4 has a 64-bit ARMv8 CPU, so "aarch64"/"arm64" is the most suitable architecture for it, although it's capable of running an 32-bit "armv7h" OS as well. (Similar to how 64-bit amd64 PCs can still run a 32-bit x86 OS.)

"AArch64" and "ARM64" refer to the same thing.

AArch64 is the 64-bit state introduced in the Armv8-A architecture. The 32-bit state which is backwards compatible with Armv7-A and previous 32-bit Arm architectures is referred to as AArch32. Therefore the GNU triplet for the 64-bit ISA is aarch64. The Linux kernel community chose to call their port of the kernel to this architecture arm64 rather than aarch64, so that's where some of the arm64 usage comes from.

The Apple-developed backend for AArch64 was called "ARM64" whereas the LLVM community-developed backend was called "AArch64" (as it is the canonical name for the 64-bit ISA). The two were merged in 2014 and the backend now is called "AArch64".

See Differences between arm64 and aarch64. AArch64 and arm64 are the same thing. Does executing the binary not work for you?

Your question could be interpreted as pretty broad, but I think what you're actually asking about is extremely specific. The fundamental difference between the different implementations of arm64 vs. aarch64.

At the heart of your question is that different CPUs provide different instruction sets. I typically reference this Wikipedia page titled: List of instruction sets, since it's the most complete list I've ever seen on the Internet.

Instruction sets

At the heart of every microprocessor is a set of instructions that it can perform. The interface to the instruction sets is what compilers convert higher level programming languages, such as C/C++, down to machine code. This machine code is the instructions from a CPU's instruction set. Incidentally instructions in an instruction set typically look like this:

    extern printf
    global main

    section .text
main
    mov eax, dword [_a]
    mov ecx, dword [_b]
    push    ecx
    push    eax

    and     eax, ecx
    mov ebx, _opand
    call    out_ops

NOTE: You'll also hear machine code referred to as assembly language.

arm64 vs. aarch64

With these 2 architectures I was able to find this answer from SO: titled: Differences between arm64 and aarch64, which stated the difference as follows:

AArch64 is the 64-bit state introduced in the Armv8-A architecture. The 32-bit state which is backwards compatible with Armv7-A and previous 32-bit Arm architectures is referred to as AArch32. Therefore the GNU triplet for the 64-bit ISA is aarch64. The Linux kernel community chose to call their port of the kernel to this architecture arm64 rather than aarch64, so that's where some of the arm64 usage comes from.

As far as I know the Apple backend for aarch64 was called arm64 whereas the LLVM community-developed backend was called aarch64 (as it is the canonical name for the 64-bit ISA) and later the two were merged and the backend now is called aarch64.

So aarch64 and arm64 refer to the same thing.

Some of your questions

You're asking questions that are too numerous to answer in a single question. I'll try and answer the most important though.

Q4. What makes me confused is the reason why archlinuxarm community doesn't provide stage rootfs tarball for only arm64 armel and etc. instead of different vendors' different products? Is it means that for example instruction set in DragonBoard 410c is different from Raspberry Pi 3? Or in other word, If I install Archlinuxarm for DragonBoard 410c to Raspberry Pi 3, What will happen? Can it boot properly?

For the specifics on this, you'd have to ask the Arch community why they opt to do things within that project. In terms of your question about running Archlinuxarm built specifically for the 410c on a Raspberry Pi 3, my suggestion would be to try it.

Both of those CPUs are ARM processors as shown here:

So my expectation would be that you'd be able to use the same binaries on both. Lastly I'd likely as a follow-up question on the Raspberry Pi Stackexchange site. There are numerous questions along the lines of what you're asking there, for example:

• What instruction set is used on the Pi's ARM/Broadcom chip?

References

• Linux on AArch64 ARM 64-bit Architecture - LinuxCon 2012
• Raspberry Pi 3 vs DragonBoard

I suggest using:

dpkg --print-architecture