I've found that there are two different properties of the order in Magento API available.
order_id and order_increment_id. For sample order they can be something like order_increment_id=100000080 and order_id=81.
The Question Is: What is the difference between them? How they are considered to be used? In the web store UI I see that my order has "Order #" = 100000080. What is order_id property for?