To me, they're slightly different from each other, but not different enough that it'd raise eyebrows to use them interchangeably. I view "shared interests" between people, groups, etc. as interests in things that they're working for, want to get, etc. For example, if my friend and I were working on a car, you could say that we share an interest in auto repair. "Common interest" would be more of interests in ideals. For example, my friend and I have a common interest in world peace. There's not much we can actively do to make the world a peaceful place but we would both want to see it happen.
Does that make sense? It does to me but I'm not the able to explain properly what goes on in my head a lot of times. I know how I make the distinction between the two isn't anything official or the like but it's how I view the differences between the them.