"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 Although it's grammatically correct, it seems very formal and outdated to me.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...