Different MultiSet and Heap

I don't know what different in C++ between this data structure. I know that MultiSet is a set that has many same keys, and Heap is like binary Search Tree. MultiSet/Set, I have read that C++ use interval tree for this data structure. So, what is real different between MultiSet and Heap in C++.
thanks :)

The only "heap" I know of in C++ is the algorithms: make_heap, push_heap, pop_heap, sort_heap. These are meant to be used on a vector, and enforce the properties of a heap data structure. If you don't know what a heap data structure is, you should look that up. Also, the priority_queue uses a heap structure.

Refer to your DADS:

bag (multiset): An unordered collection of values that may have duplicates.

heap: A complete tree where every node has a key more extreme (greater or less) than or equal to the key of its parent. Usually understood to be a binary heap.

A heap is not like a binary search tree. Yes internally it has a notion of parent/child relationships and a multiset may be implemented that way, but that's about where the similarity ends. Externally a Binary Search Tree has O(log n) search time whereas a heap doesn't support searching so it would take O(n). A heap can tell you the minimum item immediately. A binary search tree may have to visit a lot of nodes to do so. A BST allows you to visit all items in sorted order but a heap cannot do that at all. A heap requires copying items and moving them around to perform insertion or removals, but a BST doesn't. A heap is very very different from a BST.

What you're actually doing is comparing a container with a data structure.