APM versus ACPI
APM is a BIOS program, meaning that it exists independent of the operating system. Though little development has taken place with it recently, it's still quite stable and well-supported. Essentially, it manages standby, suspend, shutdown and resume commands. Additionally it will notify the operating system of any changes to the condition of the battery and control the CPU, coming to 21 different power functions in total.
So that you don't have to go all the way into BIOS to adjust these, usually these are adjusted by frontend programs, including many of the ones reviewed in this article. The most direct of these is a series of command line functions known as APMD, the Advanced Power Management Daemon.
The “successor" to the BIOS version is ACPI, the Advanced Configuration and Power Interface. What this does is takes the power management functions and makes them the responsibility of the operating system. It divides the computer into seven different states of operation, in addition to other states of operations for processors and other devices, to simplify power management.
This is in turn controlled by its command line daemon, ACPID or Advanced Configuration and Power Interface Daemon.
These two options cannot be used at the same time—after all, they provide contradictory control over power management, APM by BIOS and ACPI by the operating system. Neither one has been found to be more efficient than the other when it comes to actual power management, so your choice is influenced more by personal taste. A single advantage of ACPI is that, more often than not, you're going to be trying out different power management programs, maybe even using different ones to control different things: managing through BIOS might just get in the way. Also, some machines cannot use APM, thus requiring ACPI.