En la práctica las dos significan lo mismo. "Ni idea" quizá sea más informal en su uso.

你好 ! "No se " = 我不知道 = I don't know "Ni idea " = I have no idea / I don't have a clue = 没有想法 祝你好运 Sofía

As it was said before, they mean the same, but in a different degree. "Saber" (to know) means to have a piece of information. I you say "no sé" (I do not know), it means that you do not have that piece of information. "Idea" (idea) aside from the obvious meaning of "idea" as a thought, it can also mean "notion", "perception" or "information that could lead to getting the answer". If you say "no tengo idea" it means that you "not only do not know, but also, you have no notion/perception/information that could lead you to know the answer", the closest way of expressing this in English would be "I do not have a clue". I hope this helps you.

Las dos frases tienen un significado similar, - "no sé" tiene un uso más formal que "ni idea".