"Must" and "don't have to" carry the same meaning.
For example, you can say:
"You must study English everyday."
or
"You have to study English everyday."
I wouldn't use "must" in day-to-day speech. Although it's grammatically correct, it seems very formal and outdated to me.
Один хрен. Чаще используется to have to , но по силе нет разницы.
Полицейский не будет убеждать лечь на пол. Он скажет это в повелительном наклонении:
Get down! Don't move!
Как то так...