new and delete are C++ specific features. They didn’t exist in C. malloc is the old school C way to do things. Most of the time, you won’t need to use it in C++.
mallocallocates uninitialized memory. The allocated memory has to be released withfree.callocis likemallocbut initializes the allocated memory with a constant (0). It needs to be freed withfree.newinitializes the allocated memory by calling the constructor (if it’s an object). Memory allocated withnewshould be released withdelete(which in turn calls the destructor). It does not need you to manually specify the size you need and cast it to the appropriate type. Thus, it’s more modern and less prone to errors.