In Pathfinder the spell Guards and Wards creates - among many other effects - magical fog inside your fortress or lair. In addition you can add one of five effects, one of which is a Gust Of Wind in a corridor. Now, does that Gust of Wind effect disperse the fog as normal fog even though it was created from the same spell and caster, or is the fog one of a kind so that it can't be dispersed by wind?
Yes, it does
The fog effect created by Guards and Wards affects all corridors in the structure protected by the spell.
Fog: Fog fills all corridors, obscuring all sight, including darkvision, beyond 5 feet. A creature within 5 feet has concealment (attacks have a 20% miss chance). Creatures farther away have total concealment (50% miss chance, and the attacker cannot use sight to locate the target).
However, the Gust of Wind effect will affect a single corridor or room, and no exception was given about how it handles the fog created by the spell. As such, if placed in a corridor (and not a room), the spell will behave normally and blow away the fog in that corridor:
In addition to the effects noted, a gust of wind can do anything that a sudden blast of wind would be expected to do. It can create a stinging spray of sand or dust, fan a large fire, overturn delicate awnings or hangings, heel over a small boat, and blow gases or vapors to the edge of its range.
This GM would have guards and wards' fog unaffected by any gust of wind
While the spell guards and wards does create a magical fog throughout the warded area, that magical fog's entire description is this:
Fog fills all corridors, obscuring all sight, including darkvision, beyond 5 feet. A creature within 5 feet has concealment (attacks have a 20% miss chance). Creatures farther away have total concealment (50% miss chance, and the attacker cannot use sight to locate the target). Saving Throw: none. Spell Resistance: no.
Later the spell says, "A dispel magic cast on a specific effect, if successful, removes only that effect."
Unlike, for example, the effect of the spell fog cloud that a "moderate wind (11+ mph) disperses… in 4 rounds [and] a strong wind (21+ mph) disperses… in 1 round" and other similar spells like obscuring mist, veil of ash, and even mind fog, there's no mention in the guards and wards spell of winds of any kind having an effect on the magical fog created by the spell guards and wards.
In short, because the guards and wards spell's magical fog effect doesn't mention being affected by wind, this GM wouldn't have the guards and wards own gust of wind effect (or, for that matter, any other gust of wind effect) "blow [the fog] vapors to the edge of its range."
This means wanderers within a guards and wards magical fog effect must tough it out or negate the fog effect with a dispel magic spell, the 6th-level spell's fog effect remaining in place in the face of any wind effect… which, to this GM, seems appropriate for a spell of its power and limited utility.
However, this player wouldn't flip the table and leave the campaign of a GM who ruled that the guards and wards spell's own gust of wind effect effectively leaves one place in his PC's stronghold fog-free like this fine answer suggests. I mean, seriously, it would take highly unusual circumstances for this player to have his PC pick the gust of wind effect when the guards and wards spell makes available deterrents that are bigger (like stinking cloud), deadlier (like suggestion), and creepier (like magic mouth).