One thing missing is the installer program, and the boot loader. No distro gives you just the tools and the info.
I would summarize the three Windows/Desktop as GUI. Or Shell and GUI.
"GNU tools" is not very precise. There is coreutils package, but mount e.g. is not a GNU tool. Also modprobe is special.
redhat.com is cautious:
Note: What is and is not included when referring to Linux is
constantly debated. For the purpose of this definition, we’re talking
about the Linux kernel in conjunction with tools, applications, and
services bundled along with it. All of these things together make the
functional operating system that most people call Linux.
Package Manager and Documentation are good points of yours. Maybe you can find a convincing way of sorting out these tools, applications and services.
This is my grouping of the 50 packages in group "base" in arch-linux. I put some common categories at the end of the lines.
bash SHELL
util-linux "SYSTEM UTILS"
coreutils "GNU FILE etc. UTILS"
bzip2,gzip,tar
dhcpcd,inetutils,iproute2,iputils,netctl NET
e2fsprogs,jfs-,reiser-,xfs- FILESYSTEM
pacman PACKAGE MANAGER
systemd-sysvcompat INIT
glibc,gcc-libs CC
gawk,perl,sed PROGRAMMING
less PAGER
man-db,man_pages,texinfo DOCU
nano,vi EDITOR
s-nail E-MAIL
findutils,grep,diffutils,file
dev-mapper
lvm2,mdadm,cryptsetup
pciutils,usbutils,sysfsutils DEVICES
procps-ng,psmisc PROCESSES
logrotate
shadow USERS
gettext TRANSLATIONS
This is a mix between technical prerequisites and basic user needs. Missing parts are GUI and the C compiler (GNU compiler collection). The gcc
command might never be needed, but in theory it is essential (tool-chain).
I tried to order from "basic" to "additional", but only roughly. The EDITOR category can be expanded to vim (or emacs), then via GUI subsystem to TEX or a "office" word program.
The "rest" is just more compiled and managed (dependencies) software packages, the applications.