Tilting At Windmills

Realism in rule mechanics or realism in setting? 
Mechanical realism brings to mind things like how the rules handle armor - does armor reduce damage, is damage tracked as a specific wound rather than lost hit points, does it take training or does experience from gold automatically get a character to the next level? Realism in the setting comes from a number of different aspects of the game not necessarily connected to combat and casting. It is reflected in a PC's social standing and a hierarchy of power rather than on the mechanics of class and level. Influence gained and respect earned, relationships established, alliances, obligations, dependencies, consequences and economics all playing a meaningful role in the advancement of the character seems a realistic thing and may involve extensive mechanics, but may also be handled by referee fiat.
It is my belief that the original designers of the White Box paid some attention to the topic of realism, balancing it against a desire for a fast, fun game reflecting incorporating elements from both history and the fantastic. The result is a game (White Box and later Editions) clearly influenced by medieval European history as well as various fantasy worlds created by various science fiction authors who inspired the original game designers. The Advanced Game includes even more complexity in the form of weapon data such as weapon verses armor type adjustments and the inclusion of spell components, all in an effort to heighten the "realistic" feel of the game.

The published world of Harn, named for an island where the first products in this line were set, is one of the more realistic RPG settings I am aware of. In terms of believability or "feel", Harn and the Harnmaster rules (any edition) include so much detail and period trappings that at times it feels like reading history rather than fantasy. The art which illustrates everything Harn suggests the middle ages in gritty historic terms rather than high fantasy. Harn is a place where the circumstances of the PC's birth matters. It is a place where diseases are a threat and wounds can fester and kill days after the fight. Harn supplements include articles on Birds, Horses, Fish and other domesticated animals and plants and wildlife, as well as castles, towns and villages drawn with an archaeologist's precision. Harn is an active product line with new releases adding to the wealth of detail concerning this realistic setting.

Chivalry & Sorcery is an older system - one of the first generation of reaction games which followed the initial release of White Box - and one which strives to address the subject of realism. Born out of a desire of its designers for more realism, especially with regard to how their make-believe characters lived when not off adventuring down the dungeon, in the hay-day of the realism movement among gamers such increased realism came to C&S in the form of integration of the PC into a quasi-historic medieval milieu or "imaginary in-game society". An effort to reduce abstractions results in C&S having more detailed combat for man-to-man rules, a system for fighting larger battles and magic(k) based on  theory from several historic and literary traditions. C&S encourages a style of play the authors term the grand campaign. In a grand campaign the passage of time is tracked and each player character has a "life" outside of adventuring. Players typically have more than one active character and may choose among their "stable" for a PC to play during a particular session. Perhaps the first choice PC for an adventure is laid-up healing or busy training or researching a spell and is therefore unavailable forcing the player to play another of their PCs.
The Grand Campaign allows for greater immersion into the milieu with associated political and economic ramifications of long term play with characters who accumulate influence, power and wealth. It also allows for a style of play which mixes adventures to locations of mystery with sessions  that emphasize role-playing the interaction of player characters and NPCs, uncovering plots and brokering deals. White Box suggested that some of this type of play may occur, but emphasized the more action elements of dungeon delving, wilderness travel and jousting one's way across the land...the stuff of high adventure! Whether tilting at windmills or playing at the game of thrones, realism can play as big, or small, a part of your milieu as is desired. This flexibility is one of the strengths of our hobby.