Content strategy differs from corporate communications strategy. Content strategy is far more than your web content or social media content or any of those things that come strictly out of the corporate marketing group. It is far more than "corporate communications."
Tactics are the actions you take to make your content effective (know your audience, brand/tone of voice, style/formatting, word choice, etc.). Strategy is developing and executing plans to attract, capture, and retain customers. Content strategy is developing and executing plans to attract, capture, and retain customers throughout all the content that an enterprise delivers, both internally and externally.
Content has three purposes: to attract, capture and retain customers. Thus, the difference between content strategy and corporate communications is the difference between the marketing silo doing the first two activities and an enterprise that's accounting for all of the content creators within that enterprise to guarantee all three goals for any business.
Ultimately, that's the difference between content strategy and corporate communications.