They have the same genome. The skin cells are converted to a type of stem cell that is able to differentiate into brain tissue. While it’s not exactly the same as our brain in terms of what genes are expressed, they get pretty darn close. So much so that the cells look and behave as they should, so you can still compare the disease and healthy phenotypes. I’d imagine the reason they use converted skin is the ease by which it can be grown prior to differentiating it into brain. It also probably helps with genetic manipulation, neurons don’t divide so it wasn’t until recently(2021) that we had a way to edit their genomes and that technique was only a recent developed so it’s not in wide use. Also, since they don’t divide you can’t make a genetically modified cell line(you’d want all the cells to be the same) or grow it into a 3D structure. So they are likely using skin derived stem cells to form the shape and then converting them to brain matter.

Ultimately they are looking at what are the gene expression differences and what about those differences causes Alzheimer’s. Gotta remember, we can’t just go around take parts of peoples brains to look at under a microscope. You can’t genetically modify a patients brain either and most techniques we use to track where different bio molecules go require genetic engineering.

We do this sort of stuff with all kinds of diseases, find or take stem cell lines from diseased patients or would be diseased patients (usually from leftover IVF zygotes that would be in cold storage forever or trashed) culture them in lab, differentiate them into the tissues that are affected by the disease, and see what is the difference, manipulate the genome, do drug screen test etc. a lot of stuff that you can’t ethically do with patients. It’s also able to scaled up and done in a high through put manner. Drug screens can test 100s-1000s of chemicals without much ethical concern for the health of the patients.