Xjyuk

I tried to check what function shift-right is bound to which extends the region right by a character by default. But C-h k says:

<right> (translated from <S-right>) runs the command right-char (found
in global-map), which is an interactive compiled Lisp function in
‘bindings.el’.

If S-right does something else than simple right then why does it say it is bound to right?

Taken from this emacs wiki page:

Emacs is set up so that the keys, particularly all the control-, meta-, alt- keybindings keep working if you inadvertantly leave the shift-lock key on. So it assumes that you were looking for the unshifted one if this is the only keybinding defined on that key. Hence it sees the shifted function key, checks to see if the shifted function key has been bound to a function and if it doesn’t find a keybinding, checks to see if there is anything bound to the unshifted key. If it finds a binding, it gives you that one instead of the one you asked for.

If an input event is not bound and contains the Shift modifier or is an uppercase character, Emacs converts it to the corresponding unshifted or lowercase event. This is discreetly documented in the Emacs Lisp manual under read-key-sequence. Unlike what the docstring of read-key-sequence says, this isn't limited to the first event in a sequence: if KEY1 is bound to a keymap (so it's a prefix key) but S-KEY1 is not bound, pressing S-KEY1 KEY2 results in an event for KEY1 KEY2. However, if S-KEY1 is a prefix key, S-KEY1 KEY2 remains unchanged even if S-KEY1 KEY2 is not bound, regardless of what KEY1 KEY2 might be bound to.

Commands can find out whether such a translation happened by checking the variable this-command-keys-shift-translated. Few commands do. The only ones I can think of are the cursor motion commands that select text when Shift is pressed, like right-char. This mechanism is handled by handle-shift-selection which is triggered for every command that has ^ in its interactive specification.