The Antithesis
The villain is in direct opposition to the hero's ideals. Good examples here are Yuji/Mahito from Jujutsu Kaisen and Batman/Joker. If Batman exists to stop crime and save everyone he can, the Joker exists to show that not everyone wants to be saved- that crime and malice doesn't always have a motive. Some people will harm others just because they think it's fun. These are great for characters with big motivations, giving them an equally dark shadow to act against them. The issue is that these types of villains tend to not endear empathy from audiences, they can comes across as cartoonish. In ttrpgs, you want your players to have some kind of emotional connection with your villains, so I'd try and inspire hate. It can be easy to make a little guy your party loves- its another trick altogether to make someone your players loathe so much they are willing to burn themselves too if it means they will never return.
The Mirror
This villain is a reflection of the hero, the same motivation but different ends. The kind of motherfucker who says "We're not so different, you and I" and means it. This can be interesting because they share a starting point, there can be an easy empathy between the two. The road untraveled. It can also be a lot of fun seeing both hero and villain trying to convince the other to walk their path.
The Twist
What if you went too far? A villain that is nearly the hero but skewed, a shared goal but willing to cross lines the hero won't. An interesting aspect when running twists is that because of their proximity to the hero, players are quick to hate them. Mirrors are far enough apart to feel different, while the twist's actions can feel like a betrayal. Funnily enough, this is the type of foil I see players turn into the most- willingly crossing a line and leaving the party. Rather than try and convince them to join like the mirror, a twist should return the vitriol. Their counterpart is weak and part of the problem. A fun variant on this is making a twist that is actually less extreme than the player to make them seem less restrained. Give a community leader speaking out against their actions who is trying to do the right thing and sees the player as someone who is lighting a powder keg and putting people in danger.
The Rival
The reverse of the mirror, they have the same goal as the hero but a different motivation. The fact that they want the same thing as the hero puts them into direct competition if not conflict. These are great for tragic storylines, because you can put players in the position of either having to betray a rival or betray their party. Either way they lose something.
The Nemesis
This isn't about goals or motivations, its personal. The nemesis fucking hates you. They want to destroy you. It might be for revenge or you are simply a symbol of what they despise. They have their own goals, but their seething hate for the player also becomes a weakness. If you can force them to choose between what they are pursuing and harming the hero, you might be able to control them. Can often present as a Mirror, but while a mirror can respect you- the nemesis is disgusted by the thought.
I am sure I am missing some. Feel free to add on if anyone has any.
The obverse of the Nemesis (and one which can share space with the Nemesis - a Professional can become a Nemesis over the course of time, and some would argue that they should), with the Professional it ISN'T personal, nor is it necessarily about any goals or motivations beyond the contractual. The Professional may hate you but that doesn't matter: it's business, and you are either the job or in the way of the job. Some incarnations of the Professional fall into the trope of "punch-clock villain", where "off the clock" they might be sociable or even friends, while others are purely antagonistic until the job is done; no fraternizing with targets/hurdles.
I categorize this in "Foil" because it really is a reflection of many player-character types, just an angle which they don't often consider: when the players get "on a job", frequently everything else bends to serve that purpose, with everything from goals and "side quests" to "considerations about the long-term ripple effects and consequences of your actions" suddenly becoming irrelevant in the face of "ok but this is our QUEST, here". They may LIKE the Chancellor or the Guildmaster or the cute mechanic or what have you, but that simply doesn't matter in the face of completing quest objectives.
But players bristle when they can't make NPCs like them.