Are the active shape model (ASM) and the shape model in AAM the same?
The answer to that is neither a straightforward yes or no, and needs some information.
The shape model in both the ASM and the AAM are the same. They are point distribution models (PDMs), i.e. you have a set of rigidly aligned points, and learn a PCA, and then you've got a statistical model of those points, which is what one would call shape model.
Now, what one commonly calls Active Shape Model is the combination of a PDM and a fitting algorithm - hence the term Active. The most simple method for that is to search along each points normal ("profile direction"), and search for the strongest edge. A slightly more elaborate method is to learn the 1D gradient profile along each points normals from the training images. Cootes describes both methods in An Introduction to Active Shape Models.
An AAM has the same PDM as an ASM to model the statistical variability of the shape, but the fitting is done differently. AAMs use the learned statistical model of the appearance for the fitting, and not the method used by ASMs.
Hence, strictly speaking, the answer to your question that is quoted above is: No, the ASM and the shape model in an AAM are not the same. An AAM does not "contain" an ASM. It contains, however, the PDM part of the ASM, and the shape model in both the ASM and AAM are the same. The shape model is fitted differently though in ASMs and AAMs.
I recommend to read the paper I linked above for more details, it's a very, very well-written and very easy to understand paper.