Operating profits and losses are actual money gained or lost.
In tax parlance it's called a "net operating loss," but it's still spending more real money than one has earned in one's business(s). That is why EBIT and EBITDA mean very different things to investors and business owners/managers. It's also why tax savings are so important; they contribute directly to cash flow. When one has an NOL, in the year of the NOL's initial occurrence, you can be sure that nowhere near enough cash flowed in the right direction. In Trump's case, $916M of his actual money flowed in the wrong direction.
"Paper losses" are what one has when a stock's price drops below the price one paid for them. They do not become actual money losses until one sells the stock. That's so for other financial instruments as well.
Trump's businesses are his own. There is no stock transaction that can account for the gains and losses because his companies stock is not traded; it's merely owned by him and his family.