Manual:Page moving

Moving a page causes the page title to change while the page id remains the same. If a redirect is created under the moved page's former page title, it will have a new page id. Pages can be moved using Special:MovePage (SpecialMovepage.php) or  (ApiMove.php).

Moving a page, and then moving it again, can create double redirects.

Database
There are two possible kinds of page move log actions: move and move_redir. The latter refers to a move over a redirect.

API
A page move log event has a "move" sub-element, e.g.

Hooks
Hooks that pertain to page moves are SpecialMovepageAfterMove (MovePageForm::doSubmit), TitleMoveComplete (Title::moveTo), and AbortMove (Title::isValidMoveOperation).