How was the status quo between the fleets maintained?

Question

Wondering that I cannot find this question, so I ask:

During a big part of the movie (several hours in universe) a small fleet of rebel ships is followed by a fleet of huge first order ships. It is said that the big ships cannot catch up, to the smaller rebel ships, but have longer lasting fuel, so in the end will catch up when the smaller ships run out of fuel. My impression was, that the distance between the fleet was constant all the time (they could see each other). Even in star wars physics that does not make any sense. There are (regardless of real world physics) just two possibilities:

1. The rebel ships are significantly faster. In this case, the distance between the fleets should increase and over time rebels should be able to escape.

2. The rebel ships are barely faster, explaining the more or less constant distance. In this case the question is, how they were able to reach a safe distance in the first place.

Also I cannot remember correctly the explanation why they cannot use their tie fighters. Something like they cannot support them over the "vast" (sight) distance.

Of course in real world physics the whole situation is ridiculous. But can anybody make sense of it even in weird star wars physics? And feel free to also make sense to other nonsensical aspects of the situation I didn't mention if you like. (For example that other ships are able to leave and rejoin the fleets without being noticed or harmed)

Edit:

Perhaps more concrete:

Did I miss anything that explains the situation in the movie?

Answer 1

It was noted by the First Order that the Resistance's smaller, more agile ships are faster than theirs. At the start of the battle, they moved away form the First Order fleet at full speed, and quickly opened up a safe distance between them. However, the Resistance was low on fuel, and running at full speed is usually less fuel efficient. So having retreated to a safe distance, the Resistance must have then reduced speed to maintain steady gap, so as to maximise fuel economy.

(Obviously it doesn't make much sense that the ships would slow down after running out of fuel in space. So a more realistic interpretation would be that they retreated at max acceleration, and then cut the acceleration down to match the First Order's once a sufficient gap has been opened. Thus when the support ships ran out of fuel, the First Order caught up and destroyed them.)

The tie fighters, including Kylo, were recalled when the Resistance retreated far enough that the First Order's ships could no longer provide effective fire support to protect them. Since they were confident that the Resistance fleet could not escape even by hyper space, the First Order was content to simply wait for them to run out of fuel rather than risk losing fighters for a quicker victory.