stack dump vs core dump

Stack dump, as the name suggests, only contains the stack information of
the executable that generated it, at the point in time it was generated.

Core dump contains information about memory and registers apart from the
stack info.

You can generate a core dump of a running executable using 'gcore' on linux or
'dumper' on cygwin.If you questions is about programatically generating core dump, you
would need to take a look atgcore's implementation to see what it does.