Wargame
Professional vs recreational: A professional wargame is a wargame that is used by a military as a serious tool for training or research. A recreational wargame is one played for fun, often in a competitive context.
Recreational wargames can cover a wide variety of subjects, from pre-historic to modern – even fantasy or sci-fi combat. Games which do not include modern armaments and tactics are of limited interest to the military, though wargames covering famous historical battles can interest military historians. As professional wargames are used to prepare officers for actual warfare, there is naturally a strong emphasis on realism and current events.
Military organizations are typically secretive about their current wargames, and this makes designing a professional wargame a challenge. The data the designers require, such as the performance characteristics of weapons or the locations of military bases, are often classified, which makes it difficult for the designers to verify that their models are accurate. Secrecy also makes it harder to disseminate corrections if the wargame has already been delivered to the clients. Then there is the small player base. Whereas a commercial wargame might have thousands or even millions of players, professional wargames tend to have small player bases, which makes it harder for the designers to acquire feedback. Consequently, errors in professional wargame models tend to persist.
Although commercial wargame designers study consumer trends and listen to player feedback, their products are usually designed and sold with a take-it-or-leave-it approach. Professional wargames, by contrast, are typically commissioned by the military that plans to use them. If a wargame is commissioned by several clients, then the designer will have to juggle their competing demands. This can lead to great complexity, high development costs, and a compromised product that satisfies nobody.
Commercial wargames are under more pressure to deliver an enjoyable experience for the players, who expect a user-friendly interface, a reasonable learning curve, exciting gameplay, and so forth. By contrast, military organizations tend to see wargaming as a tool and a chore, and players are often bluntly obliged to use whatever is provided to them.
Professional wargames that are arbitrated by an umpire or the players themselves (manual wargames) tend to have simple models and computations compared to recreational wargames. Umpires may even be allowed to make arbitrary decisions using their own expertise. One reason for this is to keep the learning curve small. Recreational wargamers tend to have a lot of wargaming experience (it is usually considered a hardcore hobby), so learning a complicated new wargame is easy if it is similar enough to ones they've already played. By contrast, military officers typically have little or no wargaming experience. A second reason is that the technical data required to design an accurate and precise model, such as the performance characteristics of a fighter jet, is often classified.

Overview: The exact definition of "wargame" varies from one writer to the next and one organization to the next. To prevent confusion, this section will establish the general definition employed by this article.

A wargame simulates an armed conflict, be it a battle, a campaign, or an entire war. Business wargames do not simulate armed conflict and thus fall outside the scope of this article.
A wargame is adversarial. There must be at least two opposing sides whose players react intelligently to each other's decisions, though there are wargames with solitaire rules to govern the actions of the non-player side(s).
A wargame does not involve the use of actual troops and armaments. This definition is used by the US Naval War College. Some writers use the term "live wargames" to refer to games that use actual troops in the field, but this article shall instead refer to these as field exercises.

Setting and scenario: A wargame must have a setting that is based on some historical era of warfare so as to establish what armaments, unit types, and doctrines the combatants may wield and the environment they fight in. A historical setting accurately depicts a real historical era of warfare. Among recreational wargamers, the most popular historical era is World War 2. Professional military wargamers prefer the modern era. A fantasy setting depicts a fictional world in which the combatants wield fictional or anachronistic armaments, but it should be similar enough to some historical era of warfare such that the combatants fight in a familiar and credible way. For instance, Warhammer Age of Sigmar has wizards and dragons, but the combat is mostly based on medieval warfare (spearmen, archers, knights, etc.). Some are also set in a hypothetical future or counterfactual past, to simulate, for example, a "World War Three" or rebellion of colonists on Mars.
A wargame's scenario describes the circumstances of the specific conflict being simulated, from the layout of the terrain to the exact composition of the fighting forces to the victory conditions of the players. Historical wargames often re-enact historical battles. Alternatively, the game may provide fictional "what-if" scenarios. One challenge in the design of historical wargames is that the scenarios may be inherently unbalanced and present one side with an unwinnable situation. In such cases, the victory conditions may be adjusted for the disadvantaged side so that they can win simply by doing better than what happened historically. Some games simply concede that the scenario is imbalanced and urge players to switch sides and play again to compare their performance. It is easier to design a balanced scenario where all players have a fair chance of winning if it is fictionalized. Board wargames usually have a fixed scenario.

Level of war: A wargame's level of war determines to the scope of the scenario, the basic unit of command, and the degree to which lower level processes are abstracted.
At the tactical level, the scenario is a single battle. The basic unit of command is an individual soldier or small group of soldiers. The time span of the scenario is in the order of minutes. At this level, the specific capabilities of the soldiers and their armaments are described in detail. An example of a tactical-level games is Flames of War, in which players use miniature figurines to represent individual soldiers, and move them around on a scale model of the battlefield.
At the operational level, the scenario is a military campaign, and the basic unit of command is a large group of soldiers. At this level, the outcomes of battles are usually determined by a simple computation.
At the strategic level, the scenario is an entire war. The player addresses higher-level concerns such as economics, research, and diplomacy. The time span of the game is in the order of months or years.

Examples: Flames of War is a tactical-level historical miniature wargame that simulates land battles during World War 2.
TACSPIEL is an operational-level professional wargame developed in the 1960s by the US Army for research into guerilla warfare.
The Sigma war games were a series of strategic-level professional wargames that sought to predict the outcome of the Vietnam War.
Hearts of Iron IV is a strategic-level computer wargame set in the mid-20th century.
Wings of War is tactical-level recreational wargame that simulates World War 1 aerial dogfights.
Star Wars: X-Wing is a fantasy wargame whose rules are based on Wings of War.
Command: Modern Operations is a computer program that serves as a platform for users to create and share their own wargame of a hypothetical real world conflict (ranging from the tactical to the strategic level) using its database of units that range from World War 2 to the near future.

Design issues: 

Realism: A wargame must simulate warfare to a reasonable degree of realism, though what counts as sufficient realism depends on the players. Military wargames need to be highly realistic because their purpose is to prepare officers for real warfare. Recreational wargames only need to be as realistic as it pleases the players, so in most recreational wargames the emphasis is on verisimilitude, i.e. the satisfactory appearance of realism. In any case, no wargame can be perfectly realistic. A wargame's design must make trade-offs between realism, playability, and fun, and function within the constraints of its medium.
Fantasy wargames arguably stretch the definition of wargaming by representing fictional or anachronistic armaments, but they may still be called wargames if they resemble real warfare to the satisfaction of the players. For example, Warhammer Fantasy Battle has wizards and dragons, but the bulk of the armaments are taken from medieval warfare (spearmen, knights, archers, etc.).
Validation is the process by which a given wargame is proven to be realistic. For historical wargames, this usually means being able to accurately recreate a certain historical battle. Validating military wargames is sometimes tricky as they are typically used to simulate hypothetical future scenarios.

Complexity: Whereas the rules of chess are relatively simple, and those of Go even simpler, with the complexity of these games an emergent property of the evolving strategic state of the board, wargames contrarily tend to have very sophisticated rules as a matter of their commitment to representing the concrete realities of (various kinds of) warfare. Generally speaking, the more realistic a wargame seeks to be, the more complicated its rules are.