Some of them are cinnamon roll like. Others are more like a brioche bread. They are not like traditional flour based cakes at all. You can also get them filled with things like cream cheese, pecan praline, strawberry filling, apple cinnamon filling, etc. Some have white sugar glaze icing, some have just granulated sugar sprinkled on. There are many different types and most people have a definite favorite.
Most bakeries don't put the baby inside anymore. I've heard it's a liability/insurance thing, I don't know if that's true though. The tradition of the baby is that at an early Mar