This has come up here in the forum a few times in the past, for example here:
The short/oversimplified explanation is Fedora has customized their Grub in such a way that it is not compatible with upstream Grub. You can switch from Fedora Grub to other Grubs by using their respective boot entries in the BIOS, but trying to boot to Fedora from Arch Grub or Arch from Fedora Grub probably will not work (as you have described).
You can toggle between the Grubs using the BIOS/UEFI boot menu like I mentioned, or try a boot manager like rEFInd.