区别确实不大。只有在代词和名词前面应该用 ну'жен(阳性），нужна'（阴性）， ну'жно（中性）,, нужны'(复数). Мне надо купить фрукты=Мне нужно купить фрукты. !!! Мне нужны фрукты.

You are right! There is no different, this words are synonyms. надо - conversational нужно - more official And other word with the same meaning: необходимо.

I would not recommend to use word "надо" this is not correct word and its even not a slang word. It is indeed in use within the native speakers but you'll not find it in literature and etc. If you wish to speak correctly at the beginning you should use words: нужно, необходимо

Update: Having thought about this question for a while, I came to another idea. To me it feels like "мне надо" means "I have to" do something for somebody else, or for getting an official permission for something. Whilst "мне нужно" sounds more like "I need it" or "I want it", I must do it because I want it. That being said, they are still swappable: "мне надо сходить к доктору" and "мне нужно сходить к доктору", "мне надо поспать" and "мне нужно поспать", "мне надо доделать работу" and "мне нужно доделать работу". They are swappable in all these 3 cases. Even more update: I was typing the previous paragraph and noticed that, indeed, the phrase "мне нужно" has two absolutely correct translations to English: one is I need and the other is I must or I have to. And the phrase "мне надо" can STILL mean "I need" or "I need to", but in most cases I would translate it as "I must" or "I have to". Hope my explanation helps you =)

Ему надо пойти в поликлинику к врачу. Утром Анне нужно пойти в магазин и купить продукты. You can't see the difference because verbs follow these words. In this case (before verbs and adverbs) you can use one of them. They are equal. But before nouns and pronouns you should use ONLY нужен (m), нужна (f), нужно (n), нужны (pl).