Back  Beyond spellcraft and spell-use are all of the details of magical politics of the mighty.

What is the distance between:  'Science', 'Magic', 'Esoterica', and 'Faith' in Dnd?
On the surface of things there is no difference between the various forms of magic... or so RAW would have you believe. But RAW were originally influenced by the great works of Arthur C. Clark.  And according to that esteemed writer and futurist, "Any sufficiently advanced technology is indistinguishable from magic."
Well here's the problem with THAT...

All mortal beings who have an opposable thumb and a forebrain, the very presumption of science and technology is that EVERYONE can learn all of the POSSIBLE tricks available or will ever be available.  Given the right training and resources, we could learn how. This is why, no matter what wonders scientists produce in a lab, from an electronic limb that amputees move using their thoughts to animal-less meat, we don't point at them and shout, "Sorcery!"   We have no idea how it's done, currently, but we sense that given time and teaching, we could do it, too. Even the most extraordinary feats, which we are entirely ignorant, we will still write off as being merely an application of science.

I think what Clarke meant was that technology and magic were the same to the uninitiated.
Technology is an egalitarian applique of the studious.  Whereas Magic is Exclusive.   All of the most amazing deeds of magic written in any book are feats both great and terrible; awful, magnificent, and unknowable because magic is the purest form of aristocracy. Not merely an accident of wealth but an inborn ability which CANNOT be shared. In any given fantasy world, you either have the ability to manipulate power ...or you don't.
Those people who attempt to learn magic, without this innate and essential ability may be able to use magical technology as a monkey with a hammer. The brute force method of magic use. We press buttons until we are lucky or we blow up... and then we remember those steps. NOT that we can replicate the ability ourselves.

So ...Why do the people in THIS world fear magic but accept alchemy? Because they presume, wrongly, that all applications of technology are created by the same form craft and science. That there is NO difference between Alchemy and Brew Potion. Or the oils and powder crafted by Create Wondrous Item. And, mechanically by USE that MIGHT be considered true - as there actually isn't a spell activated potion or oil.

So IS there a difference between the various forms of magic in this campaign?
It depends,
Are you talking about if there is a difference in HOW any one person might use to manipulate power via a given technique? Then YES.
But IF you are regarding magic as that fundamental yet essential substance that ties together all of creation? Then NO.

Types of Known Magic : Artiface, Alchemy, Sigils and Seals, Relics and Artifacts, Blood Sacrifice, Druidic Herbalism, Mentalism, Spirit Binding, Faith, Occult Mysticism