Wargames usually feature much more intricate game procedures than typical games. Eurogamers often complain that wargames are "fiddly," apparently believing there's a lot of in-game activity that bears little relevance to the main decision points for the player.
Some of this is bookkeeping work, either with papers or markers, that seeks to track some of the varied factors that affect battle outcomes in the real world such as fatigue, casualties, ammunition, fuel, etc.
Some fiddliness comes from the detailed accounting of military strength, of movement allowance and terrain effects.
Some results from intricate game phasing and procedures that try to account for weapons effects, doctrinal practice or communication.
Wargames are, indeed, rather intricate, and I think this results from a fundamental tension between design goals.
No, this is not another entry in the realism vs. playability debate, although it's related.
No, the tension is between the game designer's need to represent the decision points that the player/commander should influence and the need to provide the entertainment value of the game player as a witness to the spectacle of combat.
A real-life commander at any level has very limited means for knowing what's going on and issuing orders to try to influence the action.
During the battle of Waterloo, for example, Napoleon probably issued no more than a half-dozen orders all day. He certainly wasn't involved in any activity that remotely resembled counting combat factors, coordinating the precise configuration of attacking divisions and assessing exactly how many movement factors were needed to get everyone in position.
When Lee ordered Pickett's Charge at Gettysburg he issued only the most general guidance to Longstreet, with his biggest role being assigning the attacking divisions and specifying the point of attack. A player/Lee will be far more involved in the details.
Some of this work is, of course, a consequence of the physical limitations of a manual wargame, but not all of it is, as can be seen when you look at turn-based computer wargames which could strictly limit the player to a historical amount of control, but typically don't.
Indeed, even a manual wargame doesn't have to get down into the weeds. Is Memoir' 44 an unrealistic wargame because it doesn't have a lot of detail -- or is it actually a more realistic game because the player/commander doesn't do much more than issue general orders to attack or move here or there?
What Memoir'44 doesn't do is allow the player to witness all the activity that's going on. A unit moves, takes a shot (rolls dice) and something happens (or not) to the target. Exactly what going on when the target loses a figure and retreats a hex isn't specified. Are those losses casualties or deserters? Is the retreat orderly or a a near rout?
At the other end of the spectrum you have a game like Advanced Squad Leader, which depicts the action in excruciating detail, down to the facing of individual tank turrets, the malfunctioning of individual weapons and whether a squad passes through a building or alongside of it. The player has far more control of the action than any real-life commander could dream of. Indeed, the player has more control of each piece than the commander of that piece would have. Maneuvering a tank through a village the player controls every increment of movement, every swing of the turret, while knowing the exact lay of the land -- things even the actual tank commander couldn't do.
But it's entertaining as hell, which is why ASL is such an involving game to play. But witnessing every detail of the action comes at a considerable cost in "fiddliness." And at the end of the day, after executing a half-dozen die rolls and following several procedures you end up with a result -- which could have been expressed as "you lose a half squad and they have to rout to that patch of woods." Not all that different than Memoir '44.
Non wargames can generally dispense with a lot of details because the entertainment value of the game is heavily focused on the decisions of the players and the interactions between them. Exactly how the conflict (if there is any) or other actions are resolved is neither here nor there.
Player decision-making can be important in wargames, too, but it's not even necessarily of first importance. In many wargames the player has surprisingly little real impact on the course of the game and in most wargames there can be a lot of entertainment found in playing the game solitaire. Players of nonwargames may play the game through alone on occasion to learn the rules better or try out a strategy but I don't think they do it regularly. The game's fun is provided by the social interactions and the chance to match wits with an opponent.
On the other hand, a wargame can be very entertaining to play alone because a big chunk of its appeal is in witnessing how the action unfolds. Providing that appeal requires that the "how" be depicted and that, I think, is one of the factors that distinguish wargames from other games.