Rational IDEs are built on a foundation called the Rational Software Development Platform.
In The WebSphere/Rational IDE Stack, I talked about how WID and RAD are both built on top of the ASTK, which is built on top of Eclipse 3.0. That's correct, but there's more to the story.
As Bill points out in his comment, the ASTK and so on are actually built on top of what we call the IBM Eclipse SDK (IES). You can see a good picture of it in the IBM Redbook Patterns: Implementing Self-Service in an SOA environment on page 76: "Figure 5-4 Rational Software Development Platform products."
IBM Eclipse SDK is really an internal name. Publically, we usually refer to it as the "Rational Software Development Platform." Problem is, the IBM Rational Software Development Platform (developerWorks) is also the term we tend to use for the family of Rational IDE products. So, when we use the term, are we referring to the common code base these products are built on, or the collection of products that are all built on this code base?
In any event, if I were to redraw my WebSphere/Rational IDE stack and wanted to be more complete, like Bill describes, I would show a IBM Eclipse SDK layer between Eclipse and the ASTK. This represents the stuff we add to Eclipse. Some of the parts of the IBM Eclipse SDK are optional Eclipse packages. One example is the Eclipse Modeling Framework (EMF), which I kind of assumed was part of the Eclipse 3.0 base but which is actually an extra optional module. The EMF itself contains other parts, one of which is the Service Data Object (SDO) framework, which is gaining acceptance.
So, nothing's ever simple to explain, is it? I hope this helps.