I'm not sure if anyone is at the place to define what a boot manager is. The EFISTUB in the kernel image is the actual bootloader (which is not used by grub's linux command). Note that in the case of systemd-boot, it is a boot manager instead of a bootloader, since it doesn't boot Linux in the same way as grub does. But it is also a boot manager given the chainloader command. Like in terms of grub's linux and initrd command, it's a bootloader. Or you can see it this way, a boot manager allows you to choose either a bootloader or another boot manager to execute, while a bootloader is always for loading an OS/kernel, except when the bootloader is not just a bootloader but a 'dual-role' program like grub.

(But the boot manager itself would also be an EFI executable and it can chainload another boot manager as well.)

Apparently in the case of UEFI, boot manager is somewhat equivalent to a program where you can choose which EFI executable to execute, while bootloader would be one of the EFI executables available.

Os boot manager