Roleplaying games and wargames have drifted apart considerably over the past several decades, but they still retain common elements that sometimes go unnoticed. I've told people that roleplaying games were invented as a sort of alternate format for wargaming, but it doesn't resonate for someone who has never built an army, made an army list, and struggled to make your army live up to your expectations on the battlefield. There's no obvious connection. The most popular wargames are for 2 players and look more like very complex games of chess than the not uncommon roleplaying game tradition of improvised-theatre-with-dice. However, the two game modes are still mostly doing the same thing. A lot more wargaming happens in an RPG than many people realise, and there are many outcomes from "fast-forwarded" roleplay in wargaming.
There are 3 reasons roleplaying games and wargames are often perceived as incompatible game methods.
The first is easy, because it's literal history. Some people remember it from experience, and otherwise it's well documented. A long time ago, Gary Gygax and Dave Arneson invented roleplaying games by adding, essentially, a vaguely defined bargaining mechanic to a medieval wargame called Chainmail.
There's definite dissonance between roleplay and the remnants of wargaming in Dnd, and most people are aware of it, even if they enjoy it. I do. I love that switch from kidding around at the gaming table to setting up a battle map and miniatures and getting suddenly very serious about tactical combat. It makes every little wargame feel really important. It's all fun and games, but when the miniatures come out you know you've reached a significant plot point, or at least a random monster, and the game master wants you dead. You'd better pay attention, use every advantage you have, or else the fun and games could end here and now.
Of course, every actual wargame I play also feels like that. Anticipation is high while you set up an elaborate battlefield, and hand-select an army from a collection of miniatures, and think about why the armies have assembled to fight. It's not exactly roleplay, but the preparation for a wargame can be a very similar mental and emotional process as roleplaying how RPG characters have reached the point of combat. While an RPG compresses the emotional journey into a few hours of concentrated gameplay, a wargame stretches it over weeks and months as you assemble miniatures, paint each soldier, and assemble an army.
I say it's essentially the same emotional process because building an army is not unlike building an RPG character, and the fear of "losing" that army (or a miniature within that army) is the same as fearing for an RPG character's life. It's not literally the same, because you're usually attached to specific moments in an RPG character's life experience (because you've spent hours each week playing those moments out) compared to impressions, or just specific moments in battle, for an army. But it's the same emotional process.
It's also, maybe more obviously, essentially the same mechanical process. D&D has largely defined what combat is "supposed" to look like in an RPG, and it has some interesting traits, like no mechanism for charging, no proscribed order for range and melee attacks, and a static armour class (AC) that requires no saving throw (your armour is attacked, but you don't roll defence in response.) Lots of variations on that theme exist, but in most cases you could lift the combat from an RPG and run it as a wargame.
The inverse is generally not true. There are few wargames with stats mapping to personality traits. Some have stats like Intelligence, Wisdom, Courage, Leadership, Morale, or Cool, and these suggest personality traits but they're awfully broad compared to skill lists of something like Call of Cthulhu or even the modest list of D&D or Tales of the Valiant or Pathfinder. I do use these stats to influence in-game decisions, and I can imagine running an RPG using, say, Necromunda or Middle-earth Strategy Battle Game rules but obviously there would be lots of arbitrary rulings. A typical wargame just isn't built for the nuance of social interaction, just as an RPG is built only for skirmish battles and not mass battles.
Secondly, there are social factors. Roleplaying has evolved from a skirmish wargame set in a dungeon with unwritten and unpredictable bargaining mechanics (social interactions are hard to codify) to literally whatever you want it to be. That kind of flexibility means there can be (and often is) no structure. Wargames, on the other hand, rely on structure.
Socially, this difference often is expressed as roleplaying games that are two-thirds idle conversation and one-third gameplay, and wargames that are three-thirds tactics with zero roleplay. I call this a social difference because these differences aren't written into the rules, it's just how many players execute gameplay.
You can play roleplaying games as a tactical exercise with codified social interactions. Some published adventures help with this by providing important NPCs with answers to common and obvious questions, a dialogue tree. Some gaming groups play adventures strictly by the book, with table rules that restrict interactions to who/what/where/why/when. Every NPC is either a quest or a step toward the next combat scenario. It's a highly efficient way to get through an adventure, but it's still considered roleplay for some reason.
Similarly, there are wargames that codify in-game "social interactions" so that there's no roleplay involved. There are plenty of Frostgrave and Necromunda and Zombicide scenarios out there that involve implied social interactions, but they all happen either just before play begins, or they're expressed abstractly with objectives and combat. For example, bargaining for cool weapon upgrades goes well, just so long as you successfully defend the arms dealer. Instead of roleplaying the actual deal for better weapons, you play the wargame of your army doing the arms dealer a demonstrable favour, and are rewarded for it.
Finally, the physical setup of a wargame is tangible and definite, while the in-game setup of most roleplaying games is left deliberately undefined. In a wargame, players functionally see the whole game world. In a roleplaying game, players see nothing except what the game master tells them.
As with social interaction, a big reason for this difference is the scope of what's allowed during a game. In roleplay, you can do anything and go anywhere. There's obviously no way to create that experience as a miniature world on the table. You can set up a tavern and buy lots of terrain and inevitably you'll still be one barrel short. So we don't bother, and we leave the details up to imagination.
In a wargame, when details matter they're codified. If you've found usable loot, then it gets written on your army sheet. If that item is dropped, you place a gaming token where it fell so someone else can pick it up. The objective of the mission is confined to the current battlefield, so your army isn't going to rush to follow a lead about the chantry deep within the castle until they've breached the walls. The scope is intentionally limited, which objectively limits possibilities, but then again it also focuses gameplay.
Roleplaying games and wargames both target the same goal, even though the physical and mental process to reach that goal are often different. Both game formats tell a story, sometimes a brief "one shot" story, and other times a full "campaign" of little stories. They both usually involve conflict, because drama generally does. As a game designer, understanding what each style of game provides is useful for finding the best medium to tell a specific story. As a player, understanding these two game formats can reveal a lot about your own game preferences.