What is the difference of tex-mode and latex-mode and LaTeX-mode in emacs - emacs

Question

I am configuring AUCTeX in emacs.
Most of the configurations are put in a LaTeX-mode-hook. When I open a main.tex file, I notice that the major mode is latex-mode and my hooked configurations are not activated. I have to M-x Tex-latex-mode to activate them. But the major-mode is still latex-mode.
(add-hook 'LaTeX-mode-hook
(lambda ()
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; auctex
(setq TeX-auto-save t)
(setq TeX-parse-self t)
))
So I would like to know what is the difference of these modes and how can I turn on AUCTeX automatically when I open a *.tex file.

Answer 1

The modes provided by AUCTeX are listed at https://www.gnu.org/software/auctex/manual/auctex.html#Modes-and-Hooks and they are
plain-TeX-mode
LaTeX-mode
ams-TeX-mode
ConTeXt-mode
Texinfo-mode
docTeX-mode
Instead,
tex-mode
plain-tex-mode
latex-mode
slitex-mode
doctex-mode
(note the different capitalization) are the major modes provided by the TeX mode package shipped with Emacs.
If you want to open all *.tex files with AUCTeX LaTeX mode add this to your .emacs:
(add-to-list 'auto-mode-alist '("\\.tex$" . LaTeX-mode))
Actually, this shouldn't be necessary, because AUCTeX defines the tex-mode.el mode names as alias of its own modes.

Answer 2

TLDR: Use latex-mode or LaTeX-mode (they mean the same thing), no need to change auto-mode-alist, and use LaTeX-mode-hook for hooking into AucTeX.
Setting up AucTeX can be quite confusing, because it uses advice to override Emacs' built-in support for TeX and friends.
So, after installing AucTeX from ELPA, you should see the following in C-h f latex-mode:
This function has :override advice: ‘TeX-latex-mode’.
Same for all the other tex modes, though the list of modes that AucTeX overrides depends on the value of the TeX-modes variable.
The function LaTeX-mode is not defined in AucTeX (any more?): it's defined in core Emacs, with a cryptic comment about compatibility:
;; The following three autoloaded aliases appear to conflict with
;; AUCTeX. However, even though AUCTeX uses the mixed case variants
;; for all mode relevant variables and hooks, the invocation function
;; and setting of `major-mode' themselves need to be lowercase for
;; AUCTeX to provide a fully functional user-level replacement. So
;; these aliases should remain as they are, in particular since AUCTeX
;; users are likely to use them.
;; Note from Stef: I don't understand the above explanation, the only
;; justification I can find to keep those confusing aliases is for those
;; users who may have files annotated with -*- LaTeX -*- (e.g. because they
;; received them from someone using AUCTeX).
;;;###autoload
(defalias 'TeX-mode #'tex-mode)
;;;###autoload
(defalias 'plain-TeX-mode #'plain-tex-mode)
;;;###autoload
(defalias 'LaTeX-mode #'latex-mode)
What this all means is that, at least in 2021, you do not need to change auto-mode-alist to use AucTeX; just installing it is enough for it to override Emacs' builtin functionality.
Unfortunately, there's one last source of confusion. Even though LaTeX-mode is now mostly just a useless alias for latex-mode, it turns out that code in AucTeX that overrides latex-mode does not call latex-mode-hook (it calls LaTeX-mode-hook, which is different. So the LaTeX- variables, which are the AucTeX ones (as opposed to the lowercase ones that are builtin with Emacs), are still useful.