Here's a brief overview of IDE-based drive technologies:
These are older drive technologies. Most non-SCSI hard drives and drive controllers that you can buy today or are likely to be using are EIDE, although many of the larger drives now available are UDMA.
Bus Master DMA is a technology for increasing the speed of hard disk data transfers which requires support from the motherboard and the BIOS, and at least some support from the drive.
You can learn more at http://developer.intel.com/design/pcisets/busmastr/FAQs.htm.
Ultra-DMA has many names, but we'll just call it UDMA in here.
UDMA is a more advanced technology which provides for even faster throughput, up to 33.3 MB/s, twice that of EIDE, for much lower prices than SCSI. Many new computers come with large UDMA drives and UDMA controllers, and it's possible to add a UDMA controller card (such as the Promise Ultra33) to an existing system to boost speed, even on older non-UDMA drives.
You can learn great details about UDMA at http://www.quantum.com/src/whitepapers/ultraata/