Command denotes greater authority and formality than order,though both denote authority.
1. I placed an order with the bookshop to supply me with a copy of The Shape Of Things to Come as early as possible.
2. She gave me my orders.
1. The command if the General was not liked by many,but the whole army had to obey it.
2. They obeyed his commands.
3. I command you to leave the room immediately.