Remote desktop vs. remote display

That's not a contradiction at all, it's not either/or, to claim such indicates a lack of familiarity with the subject. When connecting to an existing session the screen resizes to whatever resolution you specify when you connect, just like if you changed resolution and hot unplugged any secondary displays. When you takeover the session logged into the console that way the console switches to the login screen. You can take the session over by logging in on the console.