Both refer to 64-bit chipsets.

ARM (Advanced RISC Machine, originally Acorn RISC Machine. RISC = Reduced Instruction Set Computer) is a compact and energy saving, not a high performance chipset. Therefore according chipsets are primarily being used in mobile and energy saving devices like smartphones, tablets, IoT,…

x64 are desktop chipsets. The x basically stands for x86, meaning this refers to 64-bit chipsets that are based on x86 desktop chipsets like the 8086, 80286 or short 286, 80386 or 386, 80486 or short 486 or the 586, also known as Pentium.

Meaning, x64 refers to desktop chipsets, basically leaning towards Intel chipsets, but these days too including the according and compatible AMD 64-bit desktop chipsets with the according instruction (command) sets on a chipset level.

The according chipsets of the x64 type are usually used in according higher performance devices like desktop PCs, higher performance notebooks or even in servers and other business class devices.