A single-hose system takes in the air from the room, cools it and puts it back into the room. A single-hose unit creates a slight negative pressure in the room it cools because it does not return all of the air it takes in from the room. A small amount is used to cool the unit and is expelled through the exhaust system. Unconditioned air from adjacent rooms is often drawn into the cooled room to compensate, and this creates a slight inefficiency in the system. A single-hose system usually cools a room down more slowly than a dual-hose system.
A dual-hose system takes in air from the outside with one hose, cools it for the room, then expels the hot air out the other hose. Because a dual-hose system takes in air from the outside, it avoids the negative pressure problem. When the outside air is cooler than the room, the dual system can cool down a room faster. However, when the outside air is warmer and more humid than the air in the room, it is less efficient than a single-hose system. A dual hose system also usually has two fans, which means that energy usage is higher, but it may cool the room faster.
(A mini-split air conditioner is less common than the other two but is sometimes considered portable. These units separate the compressor and condenser coil from the fan and evaporator coil. The compressor is located outside of the home and air handler is located inside the home. Some models come with multiple air handlers that use one compressor. Usually, each air handler cools one room. These units work more like a central air conditioner, but are less expensive. They generally require professional installation.)
all air conditioners have exhaust -- only some do not actually remove any air from your growroom. Like my window unit. It doesn't suck air from my growroom out through the back. The back is where the heat comes off of the coils...