Probably a ScriptMenuAction ("A script menu action. Base Class: MenuAction").

A MenuItem has a MenuAction, with which it is "associated". The parent of a MenuAction is the Application itself, so I think this means it has been implemented as an internal "list of functions" which can then be activated by a menu item. In other words: the Item is not the Action, you have to associate them. (That's not un-like the hot key system; in fact, it might be more than superficially similar.)

Checking MenuAction in my own version of the Help, I immediately noticed it's a superclass of "ScriptMenuAction", and since that has a list of properties that smell like meta-scripting (event listeners and such), I guess that's what one ought to use.

Fascinating. It seems there are more than 3,200 "menu actions" in InDesign! That's 73 letter size pages ...

(Although your number may vary: a large part of the list seems to be the full font list, including all its bold and italic etc. variants. Still an impressive list, tho'.)

This quick hack puts them into a selected text frame:

res = [];
for (a=0; a<app.menuActions.length; a++)
 res.push (app.menuActions[a].name+" ("+app.menuActions[a].area+")");
app.selection[0].contents = res.join("\r");

Pfff. It took half an hour and now I have 10 "Browse" items in my Paragraph panel, but I think I got it.

This event handler will show the name of the current selected paragraph. Oh sure, it's a dirty trick, but hey! it works!

function aEventHandler (parent)
{
 m = app.menus.item("Text Style List Context Menu");
 alert (m.menuItems[0].name.match(/"(.+)"/)[1] );
}

I noticed too late I could have used the $ID/xxx code but I'm not running it again. How in the world do I get rid of all those "Browse" items ...