Common vs Core - difference

Assume We have couple of libs. What is the difference between core and common library. How should be recognized and organized the responsibilites of both.

+Common
  -Class1
+Core
  -Class2
+Lib1 has : Common
+Lib2 has : Core, Common

Should Common be trurerly common(all libs use it)? Or is common only for those who need it?

What is good practice when refactoring / creating project?

I'm not really feel the diferrence between Core and Common.