SpellMasters — Enchanting vs. Alchemy

Both of those characters are more support roles when compared to mage, sorcerer, warlock, etc... And based on what you depicted wouldn't be chosen as often.
However, they both have more self sufficient roles depending on which lore you go by. Just some ideas for you.

Alchemist- makes potions like you mentioned, but also manipulates natural elements. This could be as simple as changing materials from 1 thing to another (water to wine, lead to gold, coal into diamond), manipulating the elements in something to create something else (pull the iron out of the dirt to make a weapon) or as complicated as fusing creatures together (making chimeras).

Enchanter/Enchantress- does what you mentioned, but also can disenchant magical objects or other enchantments, as well as enchant him/herself (greater intellect), enchant other people (weaken, invisibility) or creatures (calm, enlarge, enrage), enchant a place (conceal) or with enough power a whole area (enchanted forest) these things might not work if your game already has an illusionist as they are very similar, difference being most illusions are more grand but merely scare tricks, while enchantments have physical aspects that can affect other things. Also, enchantments are more permanent and stay regardless what happens to the caster.

I guess I'm not understanding the question, but I don't see the two as overlapping.

When I think alchemist, sure I think potions and making things into other things, but to me the alchemist is the science of magic. they aren't magic in and of themselves, but they know how to create and manipulate it. thus they can make potions, or use existing magic to create things. they have no inner source of generating magic, but they can corral it to do what they want.

Whereas, enchanters have intrinsic magic and are able to imbue items with said magic, but they don't have the same grasp of controlling it as an alchemist. They look for places and things to contain their magic because there is so much of it, whereas alchemist have to work with what they have and so are experts at manipulating it.

I think either would work in a game about Wizards. The important thing is having the class clearly defined. Like "Wizards do offensive fire magic", "Enchanters affect properties of objects or people", "Alchemists make potions". They would all fit well, but I think you want to be sure that the classes are distinct. If there's not THAT much difference between the Enchanter and your other class(es), then I'd say go with the Alchemist, who is clearly very different and will give a totally different play experience.

I was just saying you could use both, they only overlap in certain lores/games. It all depends on what you decide for your game.
It sounds like you're leaning towards the enchanter, and you may have found your answer already.

But if you're still not sure, look up Full-metal Alchemist, it's essentially rune magic with scientific elements to create "spells"