They are both described as “must do/ have to do” but actually the shorter version is described as the long form?
This is a very good question!
Actually, in this case, we refer to both, なければ and なくては parts as long (opposed to their “short” contractions “なきゃ” and “なくちゃ”. This is a bit confusing since the polite form is also very often called the “long-form”. I will try to improve the nuance
When it comes to the actual difference between the two, this might help:
なくてはならない and なければならない are like analogous to なくてはいけない and なければならない.
I hope it helps,
That helps. Thanks!