Adventure Path Charter Subscriber; Pathfinder Rulebook, Starfinder Adventure Path, Starfinder Roleplaying Game, Starfinder Society Subscriber
Distance: "A distance weapon has double the range increment of other weapons of its kind." (emphasis mine)
Deadeye: "At 1st level, the gunslinger can resolve an attack against touch AC instead of normal AC when firing beyond her firearm's first range increment. Performing this deed costs 1 grit point per range increment beyond the first. The gunslinger still takes the –2 penalty on attack rolls for each range increment beyond the first when she performs this deed." (emphasis mine)
Distance doubles the range increment of the pistol from 20 ft to 40 ft. The deadeye deed uses the 40 ft range increment for that pistol when used.
This is why distance is pretty much a "must have" on firearms.