raster-retrace | Image tracing command line utility | Graphics library

I've been using a data structure which the original developer called a heap, it's used to implement a priority queue.

While there is a lot written about binary trees, (min/max) heaps seem less well defined (details vary between implementations).

Some characteristics I've noticed that don't necessarily apply to binary-tree structures.

• The same element can be in the queue multiple times without causing complication in execution or implementation.
• Searching (while possible and faster than an exhaustive search), is not so efficient (since the child elements of each node don't have to be balanced).
• Since searching is not efficient and there is a potential for duplicates, removal may require storing a reference to the node, instead of using a key to look-up the node (which is common practice for binary trees).
• Changing priorities in the heap is trivial, compared to a binary tree where it's most common to delete+insert.
  (with a better best case and a worse worst case compared to binary-trees)

Is there more detailed terminology for data structures that match these characteristics?
Or is it simply a min/max heap which happens to be used as a priority-queue?

Note, heres a link to a min-heap that has the characteristics described above.