They are actually three things.
The original Bumblebee project came first. It was written in Bash.
As things grew messy the original Bumblebee developer (MrMEEE) started Ironhide as a fork of the original project, layering on Ubuntu-specific configuration tools. As of Jan 2011, MrMEEE is currently less involved with the project due to his
$DAYJOB but hopes to continue work on it at some point.
Bumblebee became The Bumblebee Project (TBP), now maintained by new developers starting with a complete rewrite in C. Development is still relatively active but the future of the project seems bright.
The following extract shows the relationship between the latter two projects as they forked out of the first. You can read a lot more about the history on The Bumblebee Project's history page but you should note that it is written by the new Bumblebee maintainers. There is bad
We decided to rewrite the old MrMEEE/bumblebee codebase which contained some design flaws. We established a new development architecture, a managed organization and started to rewrite everything from scratch. During this process, we got rid of the online database. This allowed for a more secure, offline installation. MrMEEE decided not to take part in this project and instead removed support for distributions other than Ubuntu and continued with the name Ironhide. We continued with the name "Bumblebee", and use TBP/Bumblebee (TBP = The Bumblebee Project) to distinguish from the legacy MrMEEE/bumblebee project.
Unfortunately, this led to the belief that Bumblebee was dead and that Ironhide is better or even "deprecates" TBP/Bumblebee. Although the configuration database is quite horrible (it downloads unconfirmed scripts which can contain even malicious or incomplete code), it sometimes just "works". The Bumblebee Project team decided not to enable such a feature by default because we are focused on stability and do not want to give users a bad experience. A lot issues on https://github.com/MrMEEE/ironhide/issues are a result of misconfiguration of ACPI calls.
If you listen to them, you want to be using the latest Bumblebee (TBP). If you listen to MrMEEE you probably want to be using TBP (for the moment until he can maintain his project again).