Strategy Consulting is just a type of management consulting. As the name would suggest, strategy consulting entails with defining the strategy for a company/division/geography, usually in facing a specific problem (e.g. how should we enter this market?).
There are many other types of "management consulting" which are done by both MBB and by other firms. For example:
- Organisational Consulting: Recommendations on organisational aspects - e.g. how to structure organisation, defining accountability/responsibility, etc.
- Operational Consulting: Anything which advises on how to optimise/improve operations of a business - e.g. optimising supply chain.
- "PMO (Project Management Office) projects: Helping set up and run a PMO at a company to track performance using KPIs of either overall company or specific initiatives/programmes
Hope that helps!