The difference between CPAP (Continuous Positive Airway Pressure) and APAP (Automatically-adjusting Positive Airway Pressure) relates to how the pressure required to hold the upper airway open is determined. Remember that positive airway pressure, the PAP part, works the same in both cases. PAP works primarily by maintaining a distending pressure on the inside of the airway that is higher than the pressure tending to collapse the airway. Both CPAP and APAP machines have a blower-pump that creates the pressure which is delivered to your airway by a hose that connects to a mask over your nose or nose and mouth. The difference is that with CPAP a single pressure level is set by your physician based on a determination of the average or maximum pressure you require to prevent your apneas and hypopneas. This determination has typically been done by a technician while you are sleeping in a laboratory, often in the second half of the diagnostic study (in which case it is called a "split night" study).
Recently PAP devices have been developed which can, minute by minute, automatically adjust (thus the APAP), the pressure required to keep your airway open. Recorders in these machines can keep track of the average pressure you need while sleeping at home over several nights. This pressure can then be used to set your CPAP machine pressure level. The APAP machine can also be used as your permanent treatment machine, although these APAP machines are currently somewhat more expensive than CPAP equipment.
APAP has the theoretical advantage of adjusting the airway pressure to that needed at any time as conditions change during the night. For example more pressure is usually required when someone is sleeping on his/her back, or in REM sleep. Things such as weight loss or gain can change the average pressure requirement over a period of months or years. However for most patients a CPAP unit with a single pressure, set either by an in-laboratory titration or by the use of an APAP devise, is sufficient. Most studies have not shown that patient long-term use of PAP is different between the CPAP and APAP systems, although some patients have a preference for one over the other.