Giving it another go:
Extraverted Intuition makes you aware of the wider context of whatever is being perceived, allowing you to create interesting responses and alter meaning on-the-fly. From this standpoint, context is inferred from what can be observed and otherwise outwardly perceived, like following a link labelled "relevant websites".
Introverted Intuition makes you aware of all the potential frameworks that could be applied to a situation, changing the meaning by simply approaching things in a different way. You're not "looking" for a wider context in the observable world, you're shifting perspective. From this standpoint, context is inferred from the assumptions we bring into the world, like changing the lens on a camera.