The search tree is the actual search pattern in front of the shelf; from the moment one enters the aisle up to product purchase. Many different things influence the search tree, including the shopper mission, familiarity, shelf layout, brand blocking and packaging. Eye tracking is a great tool to understand the search tree, which may or may not overlap the decision tree. It quantifies the impact of each of the above-mentioned aspects on the considered set.
In a typical research setting, two or three of these aspects are measured. Metrics tell you for each of the displayed shelf layouts what is seen and what not, what is considered and what not, and what is purchased from the considered set.