Would it be okay if I attempt to explain it. Apologies if it makes no sense.
Here's the deal. Slightly simplifed:
Each human being has 46 chromosomes. That means 22 identical pairs. Then another pair which are the sex chromosomes - so either two X chromosomes for a woman, or an X and a Y for a man.
When I say 22 identical pairs, the pairs are actually not quite identical. For example each person would have two copies of chromosome 15, but they would not be completely identical copies. There would be some small differences, and mutations in the DNA in each copy of Chromosome 15.
You could say that each person has two slightly different copies of Chromosome 15 and if you were really pushing the boat out you could call them 15a and 15b.
You could go further and say that Mum has 15a:15b and Dad has 15c:5d
When a man and woman have a baby, the man contributes one copy from each of his pairs of chromosomes, and so does the woman.
So for example their DC1 might get:
Dad: chromosome 15d
Mum: chromosome 15b
but then DC2 might get:
Dad: Chromosome 15c
Mum: Chromosome 15a.
These two children would be biological siblings, but since they have no copies of chromosome 15 in common, they could be very very different people.
They could, by chance have the same thing happen with all the other chromosomes, and end up with no chromosomes in common at all.
Conversely, the siblings could all get the "a" chromosome from Mum and all the "c" chromosomes from Dad, and be born almost identical, inspite of not being twins.
Sorry this is getting terribly complicated but stick with me.
Coming to the twins who married the other twins,
Imagine that the Mum twins were a:c for all chromosomes.
and the Dad twins being from a totally different family were g:k for all chromosomes (very different from the Mum twins because they are from a totally different family., but identical to each other.)
When the Mum twins and the Dad twins produce babies, the babies could all be:
a : k for all chromosomes and so largely identical
But equally the babies of one couple ould be a : k while the the babies of the other couple could be c : g.
If this happened then the babies would be very very different from each other, but technically just as identical as siblings who also happen to
inherit a : k and c : g from their parents.
Sorry that turned out to be really complicated to explain. I hope it sort of made sense.
I'm an expert on fern sex, which is why I think a lot about this stuff.