Can I put a window a/c through the wall?
Apparently window and wall a/c units are not interchangeable, although
I don't have the details of the difference.

EDIT Window units are designed to take advantage of the fact that a window is a thin partition; vents on the outside of the a/c case can be close to the inside part of the a/c unit, but still be outside (where they have to be). This may allow the window units to be cheaper. In contrast a wall can be 6" thick or more; wall units must have all vents close to the back of the unit. BTW I always thought that the vents in the side of a window unit were for intake of air at ambient temperature to then be directed through the condenser coil at the back plane of the unit to be exhausted out the back (now hotter than ambient), but in fact some of the side vent area may also be used for expelling air which cools motors. It could be that in a window unit the venting on one side is devoted to intake of air for the condenser coil and the venting on the other side is for exhaust. This would prevent the hot exhaust air being pulled in the intake for the condenser cooling air.     


  Window ACs vs. Through-the-Wall ACs
  
  It's easy to compare window and thru-wall ACs, because they're similar
  in cooling capacity and size, but through-the-wall units tend to be
  slightly more efficient because they create an airtight seal in the
  room.
  
  The major differences between these ACs involve installation and
  venting. Window ACs fit through a window and don’t require permanent
  installation, while thru-wall ACs are actually built into the
  wall—making them popular in rooms without windows or for people who
  prefer to leave their windows alone.
  
  Wall air conditioners typically only vent warm air through the back of
  the unit, while window ACs vent from the sides and back. For this
  reason, window and thru-wall models are not interchangeable (even if
  they're the same size). In most cases, if a window unit vents out its
  side, the wall will block the vents and cause overheating. Select
  window AC models can be installed through a wall, but only if they
  have a slide-out chassis wall sleeve. Read more on wall sleeves.


https://www.sylvane.com/thru-wall-air-conditioner-buying-guide.html#vs
.