Why does a hammer and feather hit the surface of the moon at the same time?

I've been trying to figure out this concept all week!
I know:

• there is a difference between G and g
• g is an acceleration (9.8 m/s^2)
• moon has no air resistance
  Why doesn't gravity pull on the hammer more?
  How is F=m*g relevant?
  if same g, but different m, wouldn't F(orce) of gravity be the same?