The question is: what’s the difference between superb design agency and brand-consulting company?

I work in Interbrand Moscow office for more than half a year and I don’t see any differences. More particular question is: what’s the difference between Agency and Consulting company? In creative (marketing, branding, advertising etc.) areas especially I can’t see any differences. In other areas - there just no such word “agency” (there are “Management consulting” companies but no “Management agencies”).
My opinion is that company will not pay big money to “creative agency”, thats why we need Consulting companies. It’s just another brand.

What do you think?