They are not the same. Horns are found on sheep, cattle, bison, and antelope. Horns are never shed. They continue to grow throughout the animal's life. If horns are broken in a fight or accident, they don't grow back.
Horns have a porous core and a hard, strong outer surface made of keratin.
Fingernails are also made of keratin. Keratin is also present in hair, hoofs, beaks, claws, and even armadillo shells. Horns are nourished by internal blood vessels. They grow from the inside out. Most often, both male and females have horns although the male's horns are usually larger.