Icon behavior #1: Let's open an application, right-click its icon in the icons-only task list next to the menu and add it to favorites with the star icon. Repeatedly clicking the icon will now minimize and maximize that one window.

Now let's close the application, remove the icon from favorites and then add it again, however this time by dragging it from the menu down to the favorites area.

Icon behavior #2: Clicking the icon now will either spawn a new instance of the application (e.g. Terminal) or the icon will pulsate for a while but never open another instance of the application (e.g. Gnome Calendar). In any case, clicking an application icon that was favorited this way will not minimize or maximize it.

For a short demonstration, see the video of DJ Ware from minute 26:48 to 28:18 (Solus 4.2 Budgie Review)

Apologies for reporting this here, I'm aware there's a Github tracker, but for whatever reason I cannot register there with my usual mail accounts.
Edit: corrected typos.