The main difference between 1st degree murder and 2nd degree murder is how the murder was performed.
When someone is charged with 1st degree murder it means that the murder which was intentional is murder that is willful and premeditated with malice aforethought.
When someone is charged with 2nd degree murder it means that the murder was also intentional and performed with malice aforethought, but is not premeditated or planned in advance.
So it's basically just how the murder was performed and whether it was planned or not.