For most domestic situations there are 3 main types of air conditioning system -
Wall-mounted: By far the most common, wall-mounted units can either be 'single-split' systems, i.e. where each room/internal unit is connected to its own dedicated compressor unit outside; or 'multi-split' systems, where a more powerful external machine serves several internal units / rooms. The latter therefore requires pipe-routing considerations (chased into walls or inside trunking), although most modern properties are built with the pre-installation already in place for multi-split systems.
Floor-standing: these may also be in single or multi configurations as above, but floor-standing internal units are generally better-suited where heating is the priority, as the warm air rises from a lower level to heat the room.
Ducted systems: Air-con can also be run through ducting inside walls, the air blowing through vents in walls or ceiling for an unobtrusive / aesthetic solution. This is obviously best done during construction or major renovation of a property.