The difference between applied ethics and ethical theory is pretty simple.
IF something will happen out there in the world — then it’s applied… so, for example, the Death Penalty is an applied ethics topic.
Ethical theory is pretty much just the theory of how we make decisions concerning moral problems. They are general ideas about what to value, how to reason about ethics and the like.
So, if I tell you that you should act so as to bring about the most overall happiness — I’m telling you to act in accord with an ethical theory. If I tell you that your cat has rights, or that you shouldn’t pollute because it’s immoral to do so, I’m applying one of those theories to a ‘real’ problem.