Really, the differences are just what's said on the tin.
Strategy consulting is strategy consulting. It's a functional practice (in aggregate, the single largest functional practice area across MBB) that intersects all the major industries. Strategy consulting tends to focus on core questions of strategy that interest top management. Problem-solving in this profession is driven by an expectation to provide value-added solutions.
Financial Advisory Consulting is a cross-function, professional services suite aimed at improving the financial health and operations of corporations. I say cross-functional because the services could be ones of Strategy, but they could also be of People Organisation, IT Systems, Operations, et cetera. It is, however, industry-specific, and in this case, rather nichey within its specific industry vis-a-vis Financial Advisory Services.
In other words...
Strategy Consulting is a lot broader in industry and tends (especially at MBB) to focus on questions of paramount importance to top management. Financial Advisory Consulting on the other hand is far more limited in scope: financial advisory services firms and divisions would be their only industry concerns. And while theirs is a cross-functional expertise, the limiting scope of the single industry focus does not lend itself to the degree of variety afforded in Strategy Consulting.
First of all, I guess by strategy consulting you mean the Management Consulting. In management consulting, you have both strategic and operational projects. Some companies like Accenture have dedicated strategy groups. MBB companies have generalists who execute both strategic and operational projects.
Secondly, you should differentiate between the management consulting in financial services and financial advisory consulting:
Strategy consulting: Strategy consulting deals with all the activities of the firm, it includes positioning the company for better performance in all fields like finance, operation, analytics etc. Strategy consulting is for the overall developement of the firm.
Financial advisory consulting: Financial advisory consulting is about managing the profit and loss, judging the way to make perfect investments. It focuses exclusively on the financial point of view rather than the general point of view.