The similarity is that both air conditioners take advantage of inside and outside air to perform the air conditioning function. In case of a window unit, the A/C takes advantage of windows that are not very thick. The unit is simply placed on the windowsill. The A/C is sealed from all four sides where parts of the window touch the unit. The side gaps are filled with thin side panels. These panels are placed outside and remain uncovered. The advantage of this design is free movement of air because the ventilation louvers are placed on the top and sides.
This is the main difference but there are also differences in power. The louver helps move lots of air from the A/C. Such a design offers powerful air-conditioning capacity that can go as high as 36,000 BTU or 3 tons. If you are planning to install an A/C for a very large room then window A/C is the right choice.
The through the wall air conditioner is placed in a hole in the wall. The thickness of wall depends on the building structure. The stone or brick walls are thicker compared to simple sheet type siding walls. In this type of air conditioner, ventilation louvers in sleeves are placed only in the backside. Such a design limits the ventilation space available for the A/C. You will generally not find wall air conditioners over 14,000 BTU.
If lots of cooling power is needed in a room that does not have suitable window for a window A/C then another type of A/C should be selected. Whether you can choose window or wall A/C depends on the wall thickness. It is a good idea to first check the wall thickness of your room before buying a particular brand and model of wall or window A/C.
You can easily use these wall air conditioners if the wall thickness is same or less than that.
You will face problem if louvers are covered by the wall. There will be reduced efficiency because of the air movement restriction. The unit also pulls air using more power than necessary. Measure the wall thickness before buying an A/C. This will help you choose the right air conditioner and avoid technical problems.