Execution
How an order is filled, and at exactly what price.
A stop that fills below the level you set is a cost you never agreed to. Here, a stop and a target settle at their own price. In the terminal and in the server-side risk pass alike. The gap between your level and the tick that noticed it is our polling interval. You do not pay for our polling interval.
The one exception, and why
The account-level close-out fills at the market rather than at a level, because it has no level of its own. It is triggered by the state of the whole account, not by a price you nominated. Every order that does carry a price you chose settles at it.
Where the fill is decided
Order execution, margin and settlement run server-side. The browser shows you the same result the server reached rather than computing its own, which is what stops a client's screen and their statement from disagreeing.