Does the TV display the login? After logging on, do both displays work right? An easy fix might be to just enable auto login, but that won't help if you have multiple users.
As for the screens displaying differently on bootup, from what I've run in to personally and read online, its not an uncommon issue. The video card has a set priority of which ports output in which order. My GTX 980 seems to output the BIOS on DVI first, and then give me Windows on my Displayport monitor. I've seen other people with Nvidia cards with HDMI as their cards priority. Some motherboards have a Windows 8/8.1/10 mode that makes the board bypass the cards defaults and instead go off of Windows settings, so that may be worth a shot. Also you could try flipping the cables around and see whats booting to what screen first.
Not the best suggestions I realize but this has been a problem with multi monitor setups and Nvidia for a while now. Don't know if AMD runs in to the same issues.
*Edit. So looked around a bit more and from what I can see, in general display priority goes VGA, DVI, then HDMI on cards with no Display Port. With Displayport on a card I'm not sure if HDMI or Displayport would get priority.