Both are correct ! They are for different sections/features:
The former refers to the browser-action icon (displayed on the top-right corner of your browser-window, next to the address bar). It is only displayed if your extension registers a browser-action.
The latter refers to icons used throughout the extension and browser, as is explained quite clearly in the link you provide:
(emphasis mine)
One or more icons that represent the extension, app, or theme. You should always provide a 128×128 icon; it’s used during installation and by the Chrome Web Store. Extensions should also provide a 48×48 icon, which is used in the extensions management page (chrome://extensions). You can also specify a 16×16 icon to be used as the favicon for an extension’s pages. The 16×16 icon is also displayed in the experimental extension infobar feature.
BTW, that second link mentions icon as the property name, which was replaced in Manifest v2 by default_icon.
(“Migration to Manifest v2” guide)