They're the same thing. Chinese ink is just the dry mix, usually of lamp or bone black and a resin of some kind.
It is very good on paper.
Parchment/vellum/membrane/skin isn't paper.
Paper doesn't last as well as vellum, well, not in our climate. Paper does fine in dry dry areas. Generally Europe isn't dry and you did say 'insular art'.
That said, the Govt is now recording our laws on very high quality parchment paper, and hoping it'll last like the rest on vellum....no doubt they'll find out in five hundred years when they can or cannot read the paper
Chinese ink doesn't wash out either. Good quality Chinese ink that is, the poor stuff fades.
Lot of work making good Chinese ink, it can be made using the soot from so many different mixes. Oil, tar, bone, pine, and the binders vary from hide glue to resin.
The cheaper ones use gelatine, which is why it doesn't fix so well.
They do need care in the preparation to make properly, you can just add a bit of water and basically that'll only make paint, but you need to 'grind' the ink on the stone to get the resins in the mixture too to make proper ink, with all the ingredients suspended in a liquid.
There's a difference, paint and ink, iimmc ?
There's bound to be someone on Youtube doing tutorials on ink and vellum.
I haven't done any calligraphy in years apart from a few bits on cards for family and friends at birthdays and Christmas, etc.,
The vellum I used over ten years ago when I was working for H.S. doing Medieval stuff in castles. I left the samples with them since I had no other use for them.
I noted at the time though that the traditional bookbinders occasionally had scraps/offcuts. Might be worth having a look on their sites ? Still not cheap, but if you want to work with and recognise the real stuff, it's more economical than buying a skin from Cowley.
Of course, you could always make your own

I've done that, it's a lot of work, it's an awful lot of work.
You migtt ask Man of Tanith, he's making good skins just now. If he has a white skin he might spare you a few edge scraps to process for vellum.
M