I think you may have some interfaces mixed up.
HDMI is an interface that uses a high brandwidth digital smart connection using a cable. Version 1.3 is capable of carrying HD video and HD sound on just one cable.
HD-DVD, Blu-Ray, and network television cable and satelite networks now use HDMI with their components.
DVD's will play on next generation formats HD-DVD's and Blu-Ray's players. They also upconvert Standard DVDs to 1080i. However you can't watch any Blu-Ray disks on your current DVD player and there are very few dual-format HD-DVD/ Standard DVD discs out and don't expect many of them.
HD-DVD and Blu-Ray use a blue laser to read data where DVD uses a red laser. Since our old DVD players lack this, and many other important parts, they are unable to read HD-DVDs and Blu-Rays.
I am not sure what you mean by "Unified ones", but you can be sure that HD-DVD and Blu-Ray won't join forces, and there were talks of combo players that would handle both formats but they have yet to arive and I hear discouraging words that indicate they may never come out. So the only way you can play both of them is to have a HTPC with a Blu-Ray and HD-DVD driver in it, at least for now.