Difference between through the wall AC and wall sleeve replacement AC
A through the wall AC unit is more or less a window unit with slightly different mounting.  The heat vents out through both the sides and back of the unit.  A wall sleeve unit slides into the sleeve and vents entirely out the back.  Generally wall sleeve units are used on walls greater than 8" and through the wall units are installed in walls less than 8" thick.  If the sleeve is already there you'll need to buy a sleeve replacement unit.

See: https://www.ajmadison.com/guides/air_conditioner/wall/