Material sharing

Is it possible to have 2 objects share the same material but not the same textures?
Ive been working on a character and have a material for his skin and want to texture his face but when I apply the texture to his face it shows up on his hands. Do I need to duplicate the material and have separate materials for each object?

If they have the same material, they must also have the same texture. Click the number beside the Material’s name to make it a single user copy, then do the same for the texture.