Minimum order: means that the least you can order for that price is 1,000 units.
Minimum release quantity: the least you can have shipped is 1 at a time.
For example, if you want to buy pens.
You must order 1,000 pens to get them at the special price of 10 cents each. You sign a contract for that price. They will be shipped to you. If you don't want them all at once, you can order 1 or more, and then the rest will be shipped later. But you are committed to the contract to pay for 1,000 units, so they will be sent to you.