Before building either a content strategy or a content marketing strategy you must first have a brand strategy, which will define what first impression you want to give the customer, what type of brand you are and how it will capture the attention of your ideal audience.
Instead of looking at the difference between content strategy and content marketing strategy look at how the two can work together to make it run smoothly and deliver the best customer experience.
Think of the content strategy part as the planning aspect. That starts with the discovery phase; identifying your ideal customers, what content they consume and where they consume it. It should establish which channels you need to be across, how do these fit in with your ultimate goals and help you create sustainable and consistent messaging on every medium.
Following that, the content marketing strategy should then put the wheels in motion and distribute your content. This is the part where you find relevant bloggers, journalists etc to write about your product. It is crucial to build relationships and networks at this stage as it will help you get consistent and sustained coverage. Then you can amplify that on the relevant social channels decided in the content strategy.