A Generic Weapon is what happens when a badfic writer does not describe the weapons that characters are using. Generic Weapons commonly occur in crowd or battle scenes, where they are held by generics or bit characters. Generic Weapons tend to be very confusing to look at, since the continuum has no idea what they ought to be, and so they are simultaneously every weapon and none in particular.
A more specific variation of the general Generic Weapon is the Generic Gun. Generic Guns are used by badfic characters whose authors either don't know anything about firearms and don't care to do the research, or else simply can't be bothered to give the gun a name. Generic Guns aren't as confusing to look at as generic weapons because they are definitely firearms... they just can't seem to decide on which type.
Generic Guns, since they are generally written by people who don't know about guns, tend to behave quite erratically. They may be functional despite missing crucial parts; they may take bullets rather than cartridges (and thus somehow fire without gunpowder); they may be prone to jamming or malfunctioning in response to the Laws of Narrative Comedy or dramatic irony; they may even have unlimited ammunition.
To rescue weapons from their generic state, it is only necessary for the author to give a short description. For weapons held by minor characters or not seen in enough detail by the viewpoint character, the description can be general ("shotgun", for example); weapons with more importance may be described by using brand names ("Luger") or specific descriptions ("recurve bow"), which is especially important if the setting is historical or geographically specific, or if the weapon in question is characteristic of some group in the story. Other weapons may not be described specifically because the description is implied in the description of the characters (for example, an author writing that a Star Trek security officer is firing at something generally need not mention that he is using a phaser).
Unfortunately, some writers go much too far in the other direction, over-describing weapons and creating Swords of Sueness instead.