In the supply chain, you focus on the departments which are engaged with raw materials up to products, but in the value chain, you must focus on the processes which mainly add value to your activity and products. In value chain maybe your human resources add value and because of that when you want to analyze value chain you study all process like human resources too.
Supply Chain is the interconnection of all the processes/activities that start from the manufacturing of raw material and end when the final goods reach the final customer. Value Chain is a set of those activities which focus on creating or adding value to the product.
I think that we can say that the objective of the supply chain is customer satisfaction, while the objective of the value chain is gaining competitive advantage.