A fusion tree and a van Emde Boas (vEB) tree are both tree data structures used for associative arrays on integer keys. However, there are some differences between the two:

* A fusion tree uses a B-tree with a branching factor of w, while a vEB tree uses a recursive structure of smaller vEB trees.
* A fusion tree uses a constant-time operation that can be done on a machine word to search a node containing up to w keys, while a vEB tree uses a recursive structure of smaller vEB trees to achieve O(log log M) time complexity for predecessor and successor search operations.
* A fusion tree uses O(n) space and performs searches in O(logw n) time, which is asymptotically faster than a traditional self-balancing binary search tree and better than a vEB tree for large values of w, while a vEB tree performs all operations in O(log M) time (assuming that an M-bit operation can be performed in constant time) and has poor space efficiency.
* A vEB tree supports the operations of an ordered associative array, which includes the usual associative array operations along with two more order operations, FindNext and FindPrevious, while a fusion tree does not.
* The constant factor associated with vEB trees can be quite large, especially for small trees, and the universe of values must be integers, while fusion trees are not subject to these limitations.
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