In real life, everything from "warfare" to "engineering" to "economics" is an attempt to obtain the maximum efficiency from existing systems. For example, the concept of tactics (from individual soldiers all the way up to armies) is based almost entirely on trying to get the most results out of different maneuvers. The carnage and death of World War 1 was the result of a failure to adapt to a new system - namely, trench warfare and the advent of the machine gun. It took some intellectual overhauls to overcome the old, outdated mode of thinking and adapt to the reality of the situation. In video gaming, attempting something similar (trying to get the most out of the rules) is considered standard conduct (ranging from "min-maxing" to "pro gaming"), but is also considered very unimmersive. That is to say: you can do well at a game, or you can play a game as though you were a real person living through those experiences, but not both.
One glaring example of this effect is Metal Gear Online, the multiplayer component to MGS4, which uses modern warfare as a backdrop. This can be seen in the use of real gear and guns to try to make the universe seem more plausible. However, there are many changes that affect how well this can be carried out. Body shots do roughly 1/10th the damage of a headshot, and damage does not negatively affect the capabilities of the player-character. The aiming system is very precise, even as the player is being hit by gunfire. Some actions are much faster than others - for example, leaning is almost instantaneous, while "popping out" from behind a wall is slower. The camera is third-person, which (for example) allows players to look out from behind a wall without actually exposing their body. Grenades do minimal damage, and are really only useful for knocking people around.
The result of these simple changes (and a few more) is that the game is tactically dissimilar from real wars, despite the attempts to make it "believable". In real life, firefights are conducted through the use of things like suppressive fire and flanking. In MGO, firefights consist of acrobatic mercenaries rolling at each other, then popping up to try to get a headshot. The leaning ability's effectiveness will allow some players to "duck and weave" like an expert boxer; while their legs remain stationary during leaning, they are also basically immune to damage - while the vulnerable head is moving around too fast to be hit. In short, trying to use "real" tactics in Metal Gear Online will end up poorly because the system of MGO differs from the system of real life.
Here are some general examples of ways in which "realistic" games will often differ from the world they're trying to depict.
In real life, medics are protected under the Geneva Convention due to the fact that their role is humanitarian, rather than tactical. Soldiers saved by medics are often incapable of returning to combat, and while this is not always the case their inclusion in the Geneva Convention is based on this concept. In videogames, of course, this is hardly ever the case. Medics exist in a very active tactical role - that is, healing people while you try to shoot them. In addition, they are usually carrying weapons of their own (which is itself strips them of their protected status under the GC). Both of these things elevate the medic from a background humanitarian to a foreground tactical element that must be dealt with.
One notable example comes from Company of Heroes, where it seems at first like the medics are "accurately depicted" (players build medic stations, medics automatically run out and bring wounded soldiers back to the station). Of course, once enough wounded men are brought back to the station, they're formed into a new infantry squad - which, again, elevates them from "humanitarian" to "tactical", and justifies shooting medics and blowing up medic stations.
Another difference is the connection of injury to suppression and covering fire. In real life, the threat of being hit is what actually causes the effect of "suppression"; soldiers will avoid exposing themselves if it means they're very likely to be hit by machine gun fire and so on. In most games, especially games with regenerating health, it's usually okay to take a bullet or two if it means that you can use a sniper rifle to hit the guy in the head instantly (something that's fairly simple due to the point-and-click interface and the lack of interfering factors like bullet drop or wind). Company of Heroes includes suppression, but generally underestimates the effect of normal rifles to the point of near-uselessness except in massed groups.
This is one of the hardest issues to avert in a game. The nature of supply - starting at resource collection, moving to processing and production, and ending up in transportation to wherever it's needed - is complex enough to be a game in and of itself. However, there needs to be a system in place to govern the availability of things like personnel, vehicles, and ammunition. Many FPS games use a ticket-based/reinforcement system for personnel, and have vehicles be infinitely respawning, but limited in either how many can be on the field at once. RTS games, in contrast, have either a simplified resource system (collect gold, use gold to train soldier) or an abstracted system (capture points, get resource, use resource to train soldier). Either of these systems changes the tactical dynamic.
In Company of Heroes, for example, there is specific buildup from infantry to light vehicles to heavy vehicles, with the "fuel" resource necessary to upgrade status. This means that, rather than being solely about tactics and deployment, CoH is also about an abstract sort of resource management so that you have enough "fuel" to deploy anti-tank weapons before the enemy can start producing vehicles. While this is perfectly logical as a game system, it's also a (somewhat necessary) departure from real life. This means that, rather than emulating World War 2, Company of Heroes is a separate game that just happens to take place during World War 2 and use many similar things from it.
These are not the only ways that tactics differ. The key point here is that real-life tactics and weapons are the result of optimization and finding out what works in real life. In fiction, these generally-ineffective tactics are still brought to bear; there's no creation of weapons that would actually be optimized for the setting. For example, fantasy games show individuals running around with swords and armor while there's mages lobbing fireballs across battlefields. This generally necessitates a change to the sword-wielder to make them "balanced", which also helps to destroy the setting's believability. While things like this are almost a necessary part of game concepts, they must also be recognized for what they are: ways in which the rules of a game differ from the rules of reality, even when the game attempts to depict reality.