difference between memory management &memory allocation.do they both work together when allocation/access happens2 memory|how they are exactly related

Question

So I like to know when I call malloc what exactly happens? Since malloc must be a wrapper so some other function must called inside it may be brk or something, But what happens inside brk, all I know these are memory allocation functions that allocate memory and return non zero value if succeed. But then what is memory management.

So management if memory If I assume is simply keeping sizes of memory against there current value. so for example if I have a two malloc calls both are allocation 10 integer each have the size of allocation will be kept against current values in some table..Whats that table is called. So assume I am implementing a memory management unit is making sense. Is there any standard used in Linux for some struct that can be referred to as this table, Can I have multiple memory management units in one system means there is a parent MMU, and my MMU is just depending on some standard functions