What you are describing sounds like the "overscan" feature that most TVs still have as a souvenir from the early bulky CRT tube televisions. But nowadays, all flat screens have menu options to disable overscan, although they may use a different name for per TV manufacturer.
Double-check your TV manual, because using Kodi's calibration tool should only be the very last resort for solving this.
My 1920X1080 Polaroid flatscreen is of the "old" (2006) variety the settings don't even get close.
I have to go to settings set to Expert. All the way at the bottom is Video Calibration. Click it; press the down arrow until you starty seeing the corner marker and get it to show no black above it, then press the right arrow until the marker shows no black to the left. Press OK, repeat in revers for the lower right. When that is set look at the center square, if it is not perfectly square follow direction on screen. and adjust the position of sub titles.
When everything is right click back. Done.
No one buys a new TV every year (unless perhaps you won the lottery or are a famous rapper/sportsperson/whatever). 
I found this just with an itty-bitty googling:
QuoteWithin the Picture menu there is an option for choosing the Aspect Ratio, where possible always use the Just Scan selection as this will pixel map the incoming signal exactly and thus avoid any overscan or unnecessary processing.
The other thing is in settings>display resolution changes back to 640X480 everytime there is an update, and some other times with out warning.
The square box in the center is supposed to be perfectly "square" The corners should make the screen the same aspect as the TV.
BTW, a square is a rectangle with equal sides and angles.
