AArch64 is the 64-bit state introduced in the Armv8-A architecture (https://en.wikipedia.org/wiki/ARM_architecture#ARMv8-A). 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.