Literally speaking, IDE and EIDE are obsolete protocols, but most people use the terms IDE, EIDE, ATA, and ATAPI interchangeably. The current standard is ATA-7 with an Ultra-DMA transfer rate of 133 MB/s.
Do not get ATA confused with SATA. SATA, or Serial ATA, is a completely different protocol with a completely different set of power and data connections for the drives. It is quite a bit faster and much more efficient than regular ATA. When comparing ATA and SATA, ATA is usually referred to as PATA, or Parallel ATA. As far as I know, no motherboard features SATA exclusively, so if a motherboard has SATA, it should still have PATA, as well.
So to get to the point, when someone says EIDE, IDE, ATA, ATAPI, or PATA, it's the same thing - ATA. All current motherboards should have the latest version.
Just as a side note, ATA-8 is in the works. Perhaps it will compare to SATA speeds? Even if it did, it would still be very inefficient. Not to mention the big plug (compared to the SATA connection).