I have read about memory allocation for applications and I understand that, more or less, the heap, in memory, for a given application is dynamically allocated at the startup. However, there is also another concept called a min-heap, which is a data structure organized in the form of a tree where each parent node is smaller or equal to its children.
So, my question is: What are the relationships between the heap that is allocated at startup for a given application and the min-heap data structure that includes functions commonly referred to as 'heapify' and etc? Is there any relationship or is the min-heap data structure more of a higher level programming concept? If there is no relationship, is there any reason they've been given the same name?
This may seem like a silly question for some, but it has actually stirred up a debate at work.