Potions are a purely alchemical product, created through the mixing, refining, ect, of alchemical components, bringing out their innate properties due to their imbuement by mana. While they do require skill, experience and some tools (which become more and more expensive and complex the better the potion), with preferably a sanitized alchemy lab to make them in, they do not require any training in magic or enchanting to make, and do not require mana to create.
Elixirs are potions where the effects of certain ingredients, or the whole potion, has been tweaked and enhanced via complex enchantments. Elixirs can be made by anyone with knowledge of enchanting magic and mana, but the effects are exponentially better if the enchanter is more powerful and more skilled. It should be noted that making an Elixir is more or less demultiplying the effects of a potion, and can only be done up to a point. The process is extremely complicated as the enchantments have to be applied at very specific stages of the ingredients' preparation or at specific stages of the potion, making them expensive. They are, however, incredibly stable, and have a virtually unlimited shelf life, while most potions degrade after a while (with the notable exception of those with a stasis enchantment).
Philters are not technically potions. They are, however, a liquid, so most people consider them as such. Philters are essentially liquid mana that has been subjected to a series of enchantments, or execution commands. They are very, very unstable, as instead of being grounded by the stable processes and magic code of ingredients, the mana is directly processed by a sentient made enchantment, which has some serious issues. If the enchantment is damaged, wether through time, magical interference to the liquid mana, or even just distruption spells, it can get out of control and create extremely violent and unexpected results (usually resulting in the person absorbing it dying). Additionally, if the enchantment is too powerful for the person taking the Philter, or the enchantment fails to consume the mana quickly enough before it is absorbed by whoever is taking the Philter, the person is either consumed by the power or suffers the same effects as an uncontrolled mana gem absorption, both which are extremely lethal.
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Alchemy has also enabled the creation of alchemical gunpowders. Although most of them are scarcely more advanced than medieval era black powder in terms of consistency and manufacturing standards, they are vastly more potent, with even the most basic approaching the power, weight for weight, of 21st century explosives. The more advanced ones, used by the Eris Empire and other advanced polities, have explosive potential beyond any chemical explosives ever made by 2160 Earth, and are in many ways more comparable to miniaturized nuclear devices such as the EFSN's fusion grenades.
It is worth noting that while it would be technically possible to apply the same categories used in potion making to alchemical gunpowders, it is rarely done. Gunpowders are usually housed in a much more dangerous and rougher environment than potions, and thus while potions can afford a degree of instability, gunpowder cannot. Thus, elixir equivalents, such as gunpowder boosted with enchantments, are rarely used, and when they are, strictly for elite units or the most well protected of warships, such as the Eris Empire's capital ships. Philter equivalents would be, well, just philters, and generally passed over in preference to the vastly more reliable mana gem fed enchanted/runed weaponry.
Alchemical explosives are also very much possible, but they share most of their properties with alchemical gunpowder (most of them having been developed as an offshoot of gunpowder).
In the field of general medicine, most unguents, or even herbal teas (which, truth be told, are simply very basic potions when using the right plants), can be incredibly potent, and although modern, scientific medicine does exist, it has always taken a back seat to more 'traditional' means for most of the population. Still, thanks to the Eris Empire and Gorromar, industrial medicine is becoming more and more available, and there are even rumors of potion recipes that could possibly be produced on a scale previously unheard of, using vast reaction vats and complicated machines to produce batches of thousands of doses at a time.