First, you need to understand what an instruction set is.
The instruction set is generally divided into complex instruction set CISC and compact instruction set RISC, as well as several other niche instruction sets.
The x86, used by Intel and AMD, is part of CISC. The architecture proposed by Intel is called IA32, because chips at that time all end with 86, such as 8086,80386 and so on, and this kind of architecture is called x86. Because of insufficient capacity of Intel, IBM asked for a second supplier, so Intel licensed x86 to AMD and many other manufacturers, which is why AMD exists. In the 64-bit era Intel built their own IA64, AMD built their own AMD64, and IA64 failed because it wasn't compatible with x86. The AMD64 became the current x86-64. Since the x86-64 license is with AMD, AMD and Intel cross license and AMD continues to use the x86 architecture. This is why there are AMD and Intel on the market today, both of which are compatible with x86-64 architecture. (The story is much more complicated.)
ARM architecture is based on RISC compact instruction set. Also using RISC is the MIPS architecture, which is used by Domestic Loongson. ARM itself only develops the architecture, does not design the CPU itself, and makes money from licensing. The real CPU design is qualcomm Sanxing Haisi such companies.
The reason for ARM's low power consumption is that there is no need to consider compatibility. X86 has a heavy history and sacrifices a lot of power consumption and performance for compatibility. As for AMD and Intel, there is no such thing as low power consumption. The bulldozer's inefficiency is well known, and Intel once made the Pentium 4.
In a nutshell, the correspondence is CISC<->RISC, x86<->ARM, desktop Intel/AMD<-> mobile (ARM+ Qualcomm/Heath/Apple/Samsung).
The third counterpart ARM refers to the ARM company.
In fact, in addition to x86 and ARM, there are other architectures, such as IBM's Power, ORACLE's Sparc and so on. Now there is risC-V in development.