Difference between Operations Consulting & Strategy Consulting

Strategy consulting is a subset of management consulting.

Management consulting pertains to answering questions raised by someone who manages either the whole or a part of the business. The questions can range from 'I have been facing problems in delivering my product by the due date. How can I manage my operations better?' to 'We have lost a huge chunk of market share in the last quarter. How do we fix it?' Now, there are various types of questions which an organization needs help with and each question is resolved by a specific consulting group.

How do I better manage operations in my organization - Operations Consulting
What role should IT play in my business and day-to-day operations - IT consulting
How can I optimize my HR functions such as benefits and talent management - HR consulting

Most of the above questions are raised by mid-management team members who strive to meet the year end targets set by the CXOs.

Strategy consultants usually are brought in to answer questions which are raised by CXOs and Board members.
The question that they try to answer range from 'What is the reason for drop in this years profits ?' to 'Does it make sense to acquire our nearest competitor ?'.

Thus, the different categories of consultants try to answer different set of questions and strategy consultants usually end up answering the ones which the CXOs and board members need help with.