The difference between starting an Activity from a Fragment and an Activity is how you get the context, because in both cases it has to be an activity.
From an activity:
The context is the current activity (this)
Intent intent = new Intent(this, NewActivity.class);
startActivity(intent);
From a fragment:
The context is the parent activity (getActivity()). Notice, that the fragment itself can start the activity via startActivity(), this is not necessary to be done from the activity.
Intent intent = new Intent(getActivity(), NewActivity.class);
startActivity(intent);