Different from Supply Chain Management which typically focuses solely on controlling supply chain operations to reduce costs, Supply Chain Strategy is much more broad.
Supply chain strategy is leveraging the internal operations of your company as well as your extended supply chain to meet a specific supply chain objective.
So with SCM you are trying to reduce costs, where as with supply chain strategies you are looking at every aspect of your operations and the cost benefit tradeoffs in order to backup the objectives of strategic business decisions.
Another aspect is understanding the difference between supply chain management and logistics.