@OnceUponATime101 I can only guess based on what she tells me, but we did maybe 15 assessments (to include 2nd rounds), mostly top tier schools with a couple of back ups like Mill Hill, and most of the time it was pretty usual staff that probably any child of this age can do if she's taught to - colouring, drawing, basic counting and letters/numbers recognition, puzzles, pattern recognition, ability to follow instructions, writing their names, telling a story, these are all normal milestones really, some DC are just more mature by this age than others, that's all. More selective schools probe for reading, but everything was done in engaging play settings, with toys etc.
Whereas after NLCS assessment she told me they played with some brown and white small cubes (dice?) with no letters or numbers or pictures on them and they were asked to put them on a sheet of paper (board game?) following the teacher's rules e.g. the teacher puts two on one side of the paper and she needs to put two on the other side, but she also need to pick them out according to some criteria and place them on a particular spot. She tried to explain the rules but I could not make it out. It's probably the same old pattern recognition and following instructions, or maybe just a board game, but done in a different format, with no toys and rather abstract and maybe boring for some.
They also did something with a story, but it wasn't just usual reading and asking questions. A whiteboard and some boxes were used for that task and the teacher moved boxes around but it was somehow related to the story. So, again, it's comprehension basically, but in a different format.
I must add it's only my speculation and I may be wrong and she couldn't really explain it to me clearly enough, but NLCS was our last assessment and she did tell me she never had similar tasks in any other school.