Filing Date Extensions

I'm confused.  On my state(N.C.) explanations I am told "...if you owe taxes...and have filed and paid them after the original filing you may still have to pay interest and possible penalties..." 

In another  exemplar you guys published it says: "....if you owe taxes and pay them even after the original filing date you will not receive interest and/or penalty charges."  

Which one is correct?

RW

North Carolina