Different from BinominalHeap, the sub trees of FibonacciHeap have no constraints.
BinomialHeap is a collection of Binominal Trees.
Same The sub trees of both of them are min/max heap
The operations of the Heap
Different The insert, extract minimum, delete, decrease key operations in Binomial Heap cost O(lgn)
While in Fibonacci Heap, only delete operation cost O(lgn), the others are O(1)
In Binominal Heap, combination of the trees of same order/degree is needed after each insert/extract minimum/delete operation. In order to keep the properties of the Binominal Trees/Heaps. (While doing this there will at most two trees of same order/degree). While in Fibonacci Heap, consolidate operation is only needed after extract minimum or delete operation. (Consolidate operation will combine all the trees of same degree/order in Fibonacci Heap)
When extracting minimum, Binomial Heap will prompt the sub Binomial Trees to the root list, while Fibonacci Heap needs cascading cut until the unmarked node is met.