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the difference is in their atomic structure; graphite has a hexagonal arrangement while diamond has a cubic arrangement
Diamond is covalently bonded (sp3 hybridised) with all surrounding carbon atoms forming a tetrahedral lattice whereas graphite comprises of layers of 2D sheets of carbon. With each sheet covalently bonded (sp2 hybridised) with 3 surrounding carbon atoms (graphene), the sheets are bonded by relatively weak pi bonds.
the diamond is insulator and hard where as graphite is conductor and soft in nature
The difference in structure plays a large role in their properties. Essentially, diamonds are highly crystalline (tight structure and few impurities), making them very hard, dense, transparent, etc. Graphite on the other hand forms sheets that slide past one another (as they aren't covalently bonded) and give it the dull, slick, etc. properties. There are many figures online to show the difference, which seems to help more people rather than just describing.
They are two differnet forms of carbon with structure. Diamnond is having Sp3 hybridization and is very hard..have extended tetragonal structure in 3D space...whereas graphite is having sp2 hybridization and is having palnar or layer structure..The unbonded electrons above and below teh plane forms valence bond with atoms in the next plane.....Its this weak bonk that makes graphite a good lubricant...
I just wanna add a couple of things..... As diamond is sp3 hyberdized. its all bonds are satisfied leading to the hardness...... but graphite has anisotropic properties because of its layes structure....... means graphite will exhibit different properties in different direction..... parallel to layers its soft, thus use for lubrication but perpendicular to layers graphite is relatively hard....... and both are form of carbon so for this we use the term of ALLOTROPIC FORM..... free electrons in graphite make it conductor for electricity but diamond is not a a conductor of electricity because of no free electron.... diamond and graphite both have good thermal conductivity