These are two different things. The human task handler is an integration component that is registered at the engine and communicates with the human task service. You should only register it, after that it will handle the communication between the process engine and the task service.
The task client however is a client you can use to communicate with the task service, like for example query all tasks or complete a task etc. Note that you don't need this is you use a task UI (as this will instantiate a client like this for you if you click the buttons etc.).
Kris