ATA (more recently , and supposedly correctly, known as PATA to differentiate from SATA) is also sometimes known as IDE or EIDE. So ATA=PATA=IDE=EIDE.
There have been various levels within ATA (related to the data transfer rate levels). Current disks are backwards compatible with earlier standards. Connections are made using a wide flat ribbon cable (typically grey). Originally the cables were 40 wires, but later versions (from 100MB/s transfer rate I think) required 80 wires (the extra 40 wires all being ground wires to separate the signal wires in order to avoid interference at higher transfer speeds).
ATA should not be confused with SATA which is a more recent and incompatible standard.
SCSI is yet another standard that has existed for some time. Mostly used on commercial systems for high performance. Again not compatible with ATA.
If you are getting another drive then I would recommend you get one with a 7,200 rpm speed and with a 8mb cache. Other than that get whatever you like in the way of make. Some have their favourites but I've never really had a problem with any makes and consequently can't recommend any particular one. As Batch points out the drives are the same its just some call it one and others call it another. If you look about you will find 2 main types mentioned IDE and SATA. Just make sure you get an IDE one.
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