Sorry for your (and your friend's) experience.
100% they are NOT the same thing.
Egg binding is from an egg being to big to exit the vent or not being shelled and getting stuck inside. Sometimes, from from double or more yolkers, sometimes from too much daylight. I have had this happen in NON production type hens. It is often deadly fast as it also block the vent from passing droppings and causes the hen become septic. Most birds with binding will die withing 48 hours if not resolved.
Water belly, also known as
ascites can actually be from liver issues... which can be complicated by things like excess treats, often in conjunction with some sort of genetic predisposition...
https://www.mypetchicken.com/backyard-chickens/chicken-help/All-about-Ascites-disease-H289.aspx
Internal laying- or
egg yolk peritonitis (EYP) is when the yolk is released in the body cavity instead of externally...
http://www.poultrydvm.com/condition/internal-layer
Salpingitis or lash egg is caused by an infection in the reproductive tract, most often carries poor prognosis...
https://the-chicken-chick.com/salpingitis-lash-eggs-in-backyard/
I have personally (in my own flock) seen Salpingitis in French black copper Marans, she was about 5 years old. Ascites in lavender Orpington, under 1 year (in addition to sudden death caused by liver failure in buff Orps fed excess treats posted by other members). Egg binding death in Swedish Flower Hen under 2 years. Vent prolapse in Silkie hen under 2. I have not yet experienced EYP that I am aware of. I have raised dozens of breeds, hundreds of birds... and I currently have a barred Rock who has not laid eggs in a couple years, but did begin crowing and no other symptoms
yet.
My point... sex links do seem to face more issues including reproductive cancers than most standard heritage breed birds... BUT all these things CAN happen regardless of breed. Get the breeds ya like is my best suggestion, and try many!
Nutrition is key to many things and can even influence SOME genetic factors. Not feeding
excess treats like corn which is low in protein and doesn't have the added vitamins and minerals a formulated ration does, will keep things balanced. Aim for no more than 10% of the total daily intake.
I also choose to feed "flock raiser" feed (ONLY, I never switch) which has 20% protein and provide oyster shell on the side for active layers... as excess calcium fed long term to non layers such as juveniles, molting, broody, roosters, etc.. *can* (doesn't mean will) cause kidney issues and even failure. I prefer more of my nutrients to come from protein since energy only comes from 3 sources... fat, protein, and carbs which includes fiber. 16% protein in most "layer" feed is essentially the minimum to sustain a light bodied layer like Leghorn in laying condition. Heavier breed birds like RIR and many others will do best on at least 18% protein... and 22% protein was shown to have the highest hatch rates which says to me more nutrients in the eggs my family is consuming. Please note it isn't just the protein but the amino acids it contains. Feathers are made from 90% protein and it's amino acids. Not all protein is created equal, noting chickens need some animal derived amino acids so adding in more peas or soy may not give desired effect. The amino acids are added to the mostly vegetarian feeds many of us use.
While genetics is very likely at play here... I might consider getting a necropsy at a state lab done with so many appearing so close together, if there are things not being mentioned like sour crop, going off food, or other symptoms that could be a sign of something more such as Marek's virus... just to rule out something else being missed. You are brave to open them up like that, and to help a friend out!

(oh yeah, I have seen some pics with very obvious tumors lining the reproductive track, sounds different than what you describe I think, but maybe you can find some to peek at for comparison). In poultry so many things can throw the same symptoms it can be difficult to discern.

Also, feel free to start a thread for your next necropsy and take lots of picture for some of the more experienced peeps to review with you. And some less experienced to follow and learn along the way.
I see you are here in the states so these links should be good if either of you decide to use them...
How to Send a Bird for a Necropsy
State poultry labs
For what it's worth... I'm SURE there are some hatchery sex links living long lives on here. But yes, in general I do tend to avoid HATCHERY sex links even more than hatchery high production layers like Leghorn, or Rhode Island Red... as they are selected for their sex linking capability and not longevity or being the best of of the breed... otherwise in theory... these hybrids should also bring hybrid vigor... that just is not the case so far from hatchery sex links.
There are many breeds that can produce sex linked offspring when crossed. Any barred hen to any solid non white male. Lots of folks are playing with sex linking and auto sexing breeds. So I try to stay open minded.
I don't know if this helped you at all... because the more I learn, I realize the more there is to learn and I know so little!

But actually learning about chickens has made it so much more fun and intriguing, I hope it never ends. This is the tough stuff on our hearts but hang in there on your learning adventure!