Both Ni and Si function like huge databases of associations. Ni builds associations for contexts and perspectives, while Si builds associations for sensations and images.
Si
On the basic Pi level, when Si "notices" something, it will pull up whatever memories are associated with it. For example, an Si dominant might notice a scent (say, of strawberries) and have it bring to mind any number of related experiences (gathering strawberries with family in the summer, eating strawberry pancakes, etc). via how those experiences related to the Si user and what they meant in context.
On a more complex level, an Si dominant would then subconsciously associate their perceptions as memory recognition, which will bring up multiple sensory memories... and then sift through those memories to find the one most applicable to the current situation. At that point, they end up with a model by which to operate in the new context, which explains the consistency that Si is famous for (at the moment that Si chooses the most applicable memory, it comes up with an existing perspective which makes everything clear).
Ni
On the basic Pi level, when Ni "notices" something, it will bring up the state of mind / way of thinking associated with what it notices. For example, an Ni dominant might notice a scent (say, of strawberries) and have it bring to mind any number of related associations (gathering strawberries with family in the summer, eating strawberry pancakes, etc) via how those associations related to the Ni user and what they meant in context.
On a more complex level, an Ni dominant would then subconsciously associate their perceptions as pattern recognition, which will bring up multiple perspectives... and then find a way to reconcile these perspectives together into the one answer that is most like the new condition to create a prediction. If that succeeds, they end up with a comprehensive way of looking at the entire situation, which explains the "aha" moments that Ni is famous for (at the moment that Ni manages to merge the perspectives together, it comes up with a new perspective which makes everything clear).
