At one time BDI was a part of the main emc project. It stands for "Brain Dead Install" btw. There was some disagreement on the direction of future development, so now there are 2 projects.
BDI4emc is now essentially a one man project run by Paul Corner. If you download the complete disk from this project, emc will be installed on a Debian Sarge operating system. By linux standards Sarge is ancient and official support is about to end. It lacks many of the refinements that have been added to emc2. Apparently it's possible to run emc2 on this system, but why bother?
Emc2 is the main project. If you download the complete disk from linuxcnc.org, emc2 will be installed on an Ubuntu Dapper Drake operating system. Dapper isn't exactly cutting edge linux, but it still has some life left. Development of emc2 is has really shifted into high gear in the last couple of years. Imho it's one of the best open source projects anywhere.
Afaik Sherline still supplies BDI with their machines. Not sure why. Resistance to change possibly?
Anyone who says "It only goes together one way" has no imagination.