To take care of something normally refers to a problem, or a task. Example: I have to take care of the problem Johnny has with his teacher./ I need to take care of the laundry. To need to do something only refers to an action. We don't know if you need to visit your grandmother, or solve a difficult maths problem.

in first one you need to take care for something in the second one you want to do something taking care is different from doing something the difference came from their actions