Here is a good Linkedin conversation about Digital Business Strategy and Digital Strategy.
My take on the issue: Digital Strategy is just a tactic of Digital Business Strategy.
Digital Business Strategy answers questions like:
Can, and how, Digital optimize the business model?
How does Digital impact different business practices (sales, marketing, hr, production, etc)?
In terms of KPIs: increase in sales, decrease of marketing and HR costs, optimized production, etc.
Digital Marketing Strategy answers questions like:
How can Digital marketing improve the business marketing function? What are the channels?
Consumer engagement models?
What digital marketing programs can be implemented?
How do they relate with current marketing programs?
How can we market the product on the Digital space? etc.
In terms of KPIs: increase in consumer reach, brand equity, sales, community size, community engagement %, etc.