N3
別に〜ない
べつに〜ない
Not really, Not particularly, It's not like...
別に痛くないよ。少しチクってするだけ。
It's not really painful. It just stings a little.
Explanation
「別に~ない」 means 'not particularly' or 'not really'. The speaker plays something down as not so important or serious, or removes the other person's guesses and worries. In speech it often clears up a misunderstanding: 「別に怒っていないよ」 (I'm not really angry); shows an easygoing attitude: 「別に何でもいいよ」 (Anything is fine with me); or brushes off a question: 「別に」 (Nothing). Na-adjectives and nouns take 「ではない / じゃない」.
Mixed up with
A bare 「別に」 from a young person often sounds dismissive ('whatever, leave me alone'). It is rude to elders and superiors. In formal settings say 「特に~ございません」.
「特に~ない」 is neutral and polite (nothing special). 「別に~ない」 is very colloquial, often a defence or rebuttal to someone's suspicion.