That's a good question that I can't really answer myself well. It's mostly for historical reasons. However, here's my bad summary anyway:
x86 was named after the Intel 8086 microprocessor since it introduced x86. The 8086 only supported 16-bit but Intel released another microprocessor that ran a 32-bit instruction set. That one also ended with 86 like many others so x86 became the most common family of 32-bit instruction sets out there.
Later, AMD extended x86 to support 64 bits and called it x86-64 / AMD64. That somehow became synonymous with x64 or AMD64, maybe because of Microsoft:
Microsoft and Sun Microsystems/Oracle also use term "x64", while many Linux distributions, and the BSDs also use the "amd64" term. Microsoft Windows, for example, designates its 32-bit versions as "x86" and 64-bit versions as "x64", while installation files of 64-bit Windows versions are required to be placed into a directory called "AMD64".
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