「謝らなくてもいい」と「謝る必要はない」- 何が違いますか
謝らなくてもいい and 謝る必要はない- is there any difference?
Is this what you say, when you are asking someone not to apologise for something?
Are there any other ways (formal) of saying: please, don't apologise?

Question

「謝らなくてもいい」と「謝る必要はない」- 何が違いますか
謝らなくてもいい and 謝る必要はない- is there any difference?
Is this what you say, when you are asking someone not to apologise for something? 
Are there any other ways (formal) of saying: please, don't apologise?

Answer

Both is the same meaning but 「謝る必要はない」 is more formal than 「謝らなくてもいい」.

Answer

The same.
Just like the difference between "don't have to -----" and "don't need to -----."