Open a PostgreSQL table with a million rows and query for a single value. PostgreSQL finds it in under a millisecond. Not because it scanned all million rows — because it maintained a sorted tree of keys on disk, and each comparison eliminates half the remaining candidates.
Open a directory with 100,000 files and look up a filename. The operating system finds it in microseconds. Not by scanning — by traversing a tree structure that organises filenames by their position in a sorted order.
Parse a Python expression and evaluate it. The interpreter builds a tree of nodes, traverses it in post-order, and evaluates each node as it goes.
Three different domains. Three different systems. One structure: a tree. The specific variant — B-tree, directory tree, parse tree — differs by the constraints of the storage medium. The traversal logic is the same in all three.