Differentiating these two is a bit difficult because they are really close in meaning and they can sometimes replace one another. However, we mainly use 'need to' when we indicate what the goal is and what are the necessary things we must have in order to achieve it. Look at the examples below:

Basically 'have to' is more about what we are obliged to do and there is no way around it. Look at the examples below:

These two verbs are somehow similar. They are both modal verbs and they show what needs to be done in order to achieve something. Look below: