^13 and ^p are not the same. ^13 can result in the insertion of a ¶ symbol that looks like a paragraph break but isn't.

__________________
Cheers,
Paul Edstein
[Fmr MS MVP - Word]

@macropod
In Word 2007 at least, ^13 does not result in the insertion of a pilcrow sign (HTML decimal entity 182). ^13 in the Replace With box actually inserts a non-printing formatting paragraph end mark that can later be found by placing ^13 in the Find What box. The Paragraph Marks inserted through ^13 in the Replace With box do not print. They are genuine non-printing formatting paragraph end marks.

If you know of cases when this is untrue, please give detailed examples.

How about doing a bit of research for yourself. The behaviour is well-enough documented...

__________________
Cheers,
Paul Edstein
[Fmr MS MVP - Word]

Despite what you so nicely imply, I have already researched this abundantly. And I haven’t found anything to substantiate your assertion regarding this topic. On the contrary, at Special characters you can use with Find and Replace in Word I found this:

The following characters can be used in both the Find what and Replace with boxes:
^13 or ^p Carriage return/paragraph mark

This page was written to support Office 2003. Have things changed since? Where does it say so?
Please be a little bit more helpful!