Improve 'isearch-delete-char' documentation (Bug#32990)

* doc/emacs/search.texi (Basic Isearch): Index
'isearch-delete-char', its keybinding and the isearch "input
item" concept, and define the latter.
(Error in Isearch): Clarify the different uses of DEL and
C-M-w during isearch.

* lisp/isearch.el (isearch-delete-char): Correct its
documentation and link to the Info node '(emacs)Basic Isearch'
which explains less technically how this function works in
everyday usage.

doc/emacs/search.texi

@@ -99,10 +99,18 @@ text that matches the search string---using the @code{isearch} face
 that customize this highlighting.  The current search string is also
 displayed in the echo area.
 
-  If you make a mistake typing the search string, type @key{DEL}.
+@cindex isearch input item
-Each @key{DEL} cancels the last character of the search string.
+@cindex input item, isearch
-@xref{Error in Isearch}, for more about dealing with unsuccessful
+@findex isearch-delete-char
-search.
+@kindex DEL @r{(Incremental search)}
+  If you make a mistake typing the search string, type @key{DEL}
+(@code{isearch-delete-char}).  Each @key{DEL} cancels the last input
+item entered during the search.  Emacs records a new @dfn{input item}
+whenever you type a command that changes the search string, the
+position of point, the success or failure of the search, the direction
+of the search, the position of the other end of the current search
+result, or the ``wrappedness'' of the search.  @xref{Error in
+Isearch}, for more about dealing with unsuccessful search.
 
 @cindex exit incremental search
 @cindex incremental search, exiting
@@ -283,14 +291,15 @@ string that failed to match is highlighted using the face
 @code{isearch-fail}.
 
   At this point, there are several things you can do.  If your string
-was mistyped, you can use @key{DEL} to erase some of it and correct
+was mistyped, use @key{DEL} to cancel a previous input item
-it, or you can type @kbd{M-e} and edit it.  If you like the place you
+(@pxref{Basic Isearch}), @kbd{C-M-w} to erase one character at a time,
-have found, you can type @key{RET} to remain there.  Or you can type
+or @kbd{M-e} to edit it.  If you like the place you have found, you
-@kbd{C-g}, which removes from the search string the characters that
+can type @key{RET} to remain there.  Or you can type @kbd{C-g}, which
-could not be found (the @samp{T} in @samp{FOOT}), leaving those that
+removes from the search string the characters that could not be found
-were found (the @samp{FOO} in @samp{FOOT}).  A second @kbd{C-g} at
+(the @samp{T} in @samp{FOOT}), leaving those that were found (the
-that point cancels the search entirely, returning point to where it
+@samp{FOO} in @samp{FOOT}).  A second @kbd{C-g} at that point cancels
-was when the search started.
+the search entirely, returning point to where it was when the search
+started.
 
 @cindex quitting (in search)
 @kindex C-g @r{(Incremental search)}

lisp/isearch.el

@@ -1956,11 +1956,14 @@ and reads its face argument using `hi-lock-read-face-name'."
 
 
 (defun isearch-delete-char ()
-  "Discard last input item and move point back.
+  "Undo last input item during a search.
-Last input means the last character or the last isearch command
+
-that added or deleted characters from the search string,
+An input item is the result of a command that pushes a new state
-moved point, toggled regexp mode or case-sensitivity, etc.
+of isearch (as recorded by the `isearch--state' structure) to
-If no previous match was done, just beep."
+`isearch-cmds'.  Info node `(emacs)Basic Isearch' explains when
+Emacs records a new input item.
+
+If no input items have been entered yet, just beep."
   (interactive)
   (if (null (cdr isearch-cmds))
       (ding)