Convergent evolution and parallel evolution do seem very similar, but they are each distinct as is divergent evolution. Three separate types. The main difference between the first two is the origin. Convergent evolution begins with organisms that are NOT closely related. Parallel evolution begins with organisms that are related. In both cases, they evolve similar characteristics in response to analogous environmental selection pressures. I can give you an example of convergent evolution--wings of insects vs. wings of birds--but someone else will have to give you a manifestation of parallel evolution (I can't think of one at the moment).
Others, feel free to correct/modify/elaborate on my response.