Active: a character consciously chooses to undertake an activity. This can involve forethought, planning, assistance, etc.
Instinctive: a character reacts to prevent some calamity. This is done in the moment and the circumstances preclude anything but immediate reaction.
I am using the terms loosely here; obviously, in the broader sense, a character's instincts can lead him to active abilities (for example, if my instinct is to seek revenge when I am wronged, I can seek revenge with foresight and cunning). The iconic example of the instinctive (or one might say reactive) ability is the saving throw from D&D, a last ditch attempt to salvage the character from harm.
The clear divide between active/instinctive is the role the players have in them. Active abilities are those with agency within the fiction (players, usually) influencing the fiction, whereas instinctive abilities are the fiction influencing them. If that makes even the slightest bit of sense.
Because of this difference, the systems demand different design strategies. Active abilities need to be designed in such a way that they can account for forethought, planning, assistance, etc., whereas instinctive abilities cannot.
What are some of the ways various games handle this?
Traditional RPGs: if you do a thing in a certain way, the GM might apply a bonus to your roll. Often in a binary pass/fail scenario, the difference between instinctive and active abilities is blurred. What is the difference between making a skill check to persuade the Duke and making a persuade check to avoid offending him? Not much.
Burning Wheel (et al.): FoRKs, wises, helper dice for active abilities. I don't know the system well enough to comment on its instinctive abilities except that I am uncertain that it has a separate system for them.
Apocalypse World: all abilities are active and the instinctive portion is typically wrapped up into the 7-9 results. The move made is determined by the fiction. There's also a help move. The only instinctive ability (I think) is the suffer harm move, which usually only occurs as a result of a move (thus the instinctive ability flows from the active and might be considered a hybrid form of that).
Blades in the Dark: adding +1d for a whole host of reasons. The players also have a choice to resist harm or accept the consequences.
What are your thoughts on these mechanisms, exactly?