Why is appropos (C-h a) not finding all terms, e.g. backup doesnt find make-backup-file-name-function

Question

When running C-h a then entering backup, it lists the following matches, but not all of them (e.g. does not find the make-backup-file-name-function)?

Buffer-menu-backup-unmark     M-x ... RET
   Move up and cancel all requested operations on buffer on line
   above.
diff-backup           M-x ... RET
   Diff this file with its backup file or vice versa.
dired-backup-diff         M-x ... RET
   Diff this file with its backup file or vice versa.
dired-flag-backup-files       M-x ... RET
   Flag all backup files (names ending with `~') for deletion.
ediff-backup              M-x ... RET
   Run Ediff on FILE and its backup file.
magit-wip-initial-backup-mode M-x ... RET
   Before saving a buffer for the first time, commit to a wip ref.
package-menu-backup-unmark    M-x ... RET
   Back up one line and clear any marks on that package.

Answer 1

C-h a runs apropos-command, and so will only show you interactive commands, not variables like make-backup-file-name-function. You could use apropos-user-option in combination with a non-nil value of apropos-do-all to search more extensively.

Interactively you can use a prefix argument C-u to tell most 'apropos' commands to use their apropos-do-all behaviour.

Note that M-x apropos will show matching functions, variables, and faces.