A btree is a kind of binary tree, one which is self-balancing to keep O(log n) lookups from turning into O(n) lookups which is possible without the self-balancing. (Think about a naïve binary tree where you insert elements in sorted order—then everything will be in the right (or left if you start with the maximum value) branch and you need to traverse the whole structure to find the node you're looking for.)
For sorting or adjacency queries, you want a btree index. A hash index can give you O(1) lookup with the drawback that you lose ordering completely (whereas getting a sorted selection of records with a tree is a O(1) operation). The trick here is having a hashing function which is both fast and avoids collisions (the worst case scenario is hash(x)=1 where everything hashes to the same value and you end up again with O(n) lookups).
For sorting or adjacency queries, you want a btree index. A hash index can give you O(1) lookup with the drawback that you lose ordering completely (whereas getting a sorted selection of records with a tree is a O(1) operation). The trick here is having a hashing function which is both fast and avoids collisions (the worst case scenario is hash(x)=1 where everything hashes to the same value and you end up again with O(n) lookups).