x86-64, commonly called 64-bit) is backwards compatible with
x86, so software written for the latter can run on the former. The name comes from the fact that AMD came up with it, but Intel adopted it and software for
amd64 run just fine on Intel CPUs. Since
x86 can't run software written for
Macbooks used to have CPUs of the PowerPC architecture, but they have long since shifted to the
x86-64 architecture. A separate image is offered for Macs not because of optimization, but because of booting issues caused by the UEFI implementation in Macs (see What is different about the Mac ISO image?).
Ubuntu offers three options for the
x86 (commonly called 32-bit) and its successor architecture
amd64 image, UEFI/BIOS bootable.
amd64 image, BIOS bootable (i.e., UEFI systems will boot them in the Legacy boot mode).