BinaryTree

Tree with nodes as 0,1 or 2. Because of 2 child, notion of left and right child exists here.

The height varies from logn to n, where n is the number of elements. Logn happens when the binary tree is "Full" binary tree.

Number of nodes of a full binary tree with leaves as L will be 2L-1

B-Tree

B-Tree is generalization of Binary Search Tree, but node could have more than 2 children.

The biggest advantage comes for B-Tree when one node of tree contains keys equal to the physical page size. Thus in case of searching the search complexity would be O(log_{noofNodesInAPage}n). Thus for example, one node of B-Tree stores 1000 Elements, and the complexity would become: log₁₀₀₀n which, for 1,000,000 is just 2. Thus only in 2 physical page loads, index is searched.

B+ Tree

The only difference between B-Tree and B+ tree is that in B-Tree, each node may point to actual data also. But in B+ tree, only the leave nodes would point to actual data. See: http://stackoverflow.com/a/12014474/231567 for more details.