In relativity, there is no absolute position or time. Each observer simply assigns to each point in spacetime x,y,z, and t coordinates. This is a "coordinate system". One can choose whatever coordinates system one likes, but some are more useful than others, and some are more natural than others. If A and B are 10ly away from each other, it can be observed that it takes light 20 years to travel from A to B and back again. There is no way to directly observe how long it takes light to travel from B to A. If one asserts that light travels instantaneously from B to A, but takes 20 years to go the other way, there is a coordinate system in which that is true. However, as there is no reason to think that the universe prefers certain directions, it is natural to assume that it takes light 10 years each way. A coordinates system consistent with this assumption would assign the event of light leaving B a time coordinate 10 years earlier than the event of that light arriving at A. That is:
(light leaves B)t = (light arrives at A)t - 10.
According to this coordinate system, a person calculating the speed of the ship would take the distance traveled divided by time taken, and to calculate time taken, they would take the difference in time coordinates of the two events. That is, they would take the time coordinate of the ship arriving at A, and subtract the time coordinate of it leaving B. Note that the last quantity is the time coordinate of the ship leaving B, not the time coordinate of the person on A seeing the ship leaving B. The time of an event is the time it occurs, not the time that you see it.
In relativity, the "observed" time of an event is the time coordinate that one's coordinate system assigns to that event, not the time that it is seen.