amd64 was the name originally given to AMD's 64-bit extensions to the x86 architecture. Later, Intel released their version of the extensions, which have gone under a variety of names like EM64T, IA32e, and similar. Later on, a more generic name of x86_64 came out for the 64-bit extensions of x86.
However, since the architecture was originally named amd64, FreeBSD continues to use that name for it.
Any x86 CPU that supports "Long Mode", or LM, can run the amd64 version of FreeBSD.
There's another 64-bit CPU architecture from Intel, known as IA-64. This is the instruction set used by the Itanium series of CPUs, and is not compatible with x86.
IOW, for 32-bit Intel or AMD CPUs, you can use the i386 version of FreeBSD.
For 64-bit Intel and AMD CPUs, you can use the amd64 version of FreeBSD.