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.