IDE = Integrated Drive Electronics, originally done by WD, and included an unnamed connector which was referred to as the IDE connector, eventually evolved to ATA. Every drive has integrated controller that manages it internally for a very long time (although the earliest drives had far more simplistic controllers and internal electronics; we are talking 1970s and earlier).
Used to incorrectly refer to P/ATA when discussing a connector, and used incorrectly to describe a controller's mode of operation when meant to say legacy (non AHCI).
P/ATA = Parallel Advanced Transfer Attachment. Originally just named ATA, the Parallel was added retroactively when SATA (serial ATA) arrived).
PATA/ATA is a port used to connect to a HDD.
SATA = Serial Advanced Transfer Attachment. A port used to connect to HDD. much newer and faster than ATA.
AHCI = Advanced Host Controller Interface. The is a modern standard for communication between a drive and its controller, meant to enable new capabilities in SATA type HDDs. It allows hot plugging, NCQ, TCQ, TRIM, etc... although I have heard that some companies have managed to get TRIM over legacy controller mode.
UDMA1 through5 and PIO1 through 6 = Old standards of communications which were used via ATA connectors.
IDE Mode = Tells the motherboard to use obsolete legacy method of communicating with drives for backwards compatibility purposes. This prevents the operation of certain modern capabilities, such as hot plugging, NCQ, etc.
NCQ = Native command queuing, it enables to the drive's controller to alter the order of writes according to whatever logic it wants in order to maximize performance.
TCQ = Tagged command queuing, think of it as NCQ lite, does the same thing only not as well.
Some rare drives have extremely bad NCQ implementations (usually very old drives), they simply included it as a checkbox feature, but in fact it has lowered performance instead of increasing it. In such a drive disabling AHCI will force your mobo to communicate with the HDD in legacy mode, this will prevent NCQ from working and improve performance.
In modern drives and in SSDs you want to have AHCI enabled for the improved performance drives see with NCQ.
Also, some drives would have an NCQ strategy that would slightly decrease single thread performance but greatly improve multi thread performance, this is good because multi threaded operations are common, and are where HDD bottlenecks most frequently occurs. Those can lead people to mistakingly thinking that NCQ lowered performance because they only tested single threaded performance.
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