http://myfaces.apache.org/faq.html wrote: MyFaces is a family of projects related to the JavaServer Faces (JSF) specification published as part of the Java Community Process. The "core" project is an implementation of that specification. Other MyFaces projects implement related specifications (eg the Portlet Bridge), or add features to any JSF implementation (not just the Myfaces Core).
See the documentation within the various projects for further details.
While you are correct in saying that MyFaces is a JSF implementation, MyFaces is not just a JSF implementation. The JSF standard is implemented by the MyFaces Core project. But MyFaces has a lot more sub projects, like the Trinidad and Tomahawk component sets, Orchestra, ExtVal and other extensions to the JSF standard.
If you're using MyFaces, you are using JSF. You can use the MyFaces Core project as JSF implementation, or you can use the Sun Reference Implementation, a.k.a. Mojarra. Both implement the same JSF standard, so there are very little differences between them. However, my experience is that the MyFaces Core implementation does provide better debug logging, which may be an advantage during development of your application.
Apart from a JSF implementation, you probably need some additional frameworks too. At least you need an additional set of components, as the standard JSF components are a bit bare bones. As said in my previous post, MyFaces offers such component sets in the Trinidad, Tomahawk and Tobago sub projects. There are also a lot of ohter component sets: ICEfaces, RichFaces, PrimeFaces, Oracle ADF Faces, and many more. Some are commercial packages, some are open source projects.