Extroverted Intuition (Ne) is the function associated with breadth of creativity, ingenuity, and often change. Ne is commonly associated with what it referred to as “wit”, mental sharpness and the ability to connect the dots between ideas quickly. Of all the functions, especially in the dominant slot, Ne tends to be the fastest processing of the functions. Introverted Intuition (Ni) on the other hand is the function associated with a depth of conceptual understanding, one that focuses on singular ideas instead of the connections between multiple. Intuitive functions in general are related to the idea of foresight, the ability to understand how things will unfold and in what ways events are connected.
Unlike Ni, which is more akin to an arrow seeking a long-range singular target via the prediction of the unfolding of events temporally/in relation to time, Ne instead seeks to find the relationship between ideas and events in a more immediate sense. Imagine a singular moment in time is represented by a 2-dimensional plane, like graph paper. Scattered on this plane are dots, each representing concepts and archetypal ideas that are being represented within that moment. This plane represents a singular moment in time though, and the plane and the dots on it are refreshed as fast as the human mind can perceive. Ne, starting from one point on this plane, reaches out like tendrils and connects ideas to eachother across this plane, finding associations quickly and, the higher Ne is in the stack, with relative ease. A more complete picture of singular moments in relation to conceptual understanding is painted within the mind of the Ne type as these connections are made. Ni on the other hand transforms this 2-dimensional plane by adding a third dimension, time. This transformation comes at a cost though. Instead of having the reaching tendrils of Ne that connects the various conceptual dots, Ni instead focuses on a singular, or very few, dot(s). It then explores this dot via the third dimension that was added, time. It looks at how a singular conceptual meaning might theoretically unfold throughout the third axis of time. As moments in time are represented by an infinite number of planes, each with conceptual dots across them, the singular Ni focus attempts to breach into the planes that have yet to unfold, like a vector starting on a plane that then pierces forward through the third dimension, into other planes. This third dimension could also just be conceptually understood as "depth" and doesn't necessarily have to represent time, though this is often the focus of introverted intuitive types. Ni types will place more mental effort into deeply exploring singular concepts as opposed to exploring the various connections between conceptual meanings in real time.
Below is a visual representation of this concept.
Let the x and z axis represent a moment in time, where the y axis represents the movement of time across moments.
One thing to notice is that Ne, even if it doesn't always make connections to further out thoughts/concepts, tends to notice more in the immediate sense and is generally more aware of the multitude of concepts in a situation. Ni, being more selective, is less likely to notice as many concepts as Ne but will spend more time and energy reflecting on and processing the chosen ideas.