I think the meaning of static/dynamic has changed over the years.
When talking about how the page gets served, a dynamic page is one that gets constructed on the fly, say from a database.
Originally these were identifiable by the use of query string parameters like your example page=123. The parameters gave the information so a single page could provide different data, depending on the values passed. So these URLs were called dynamic.
Another indicator of a dynamic page was that the file extension indicated the language used to generate the page. e.g. index*.php*
static pages are normally an html file that contains the pages content, pre-built, hence static.
However, it has been common practice to hide these raw URLs so that it it not obvious if the page was dynamically or statically created. The method is often referred to as rewriting the URL.
This is done so that a website can present a nicer, keyword rich URL for the search engines.