The component of the contact force parallel to the surface of contact is defined as the frictional force. But looking at the microscopic origin of the force I think it need not to be so.
Microscopically the attractive force between any two nearby atoms in contact is friction (this occurs due to the formation of cold bonds which leads to the stability of the system) whereas the repulsive force is the normal reaction.
Considering the case of a block lying on a rough surface and let's assume that the planet on which it's resting isn't performing any accelerating motion. Now clearly cold bonds would have formed (For simplicity assume that planet and the object are made up of pure metal without any coating of any type). Now when I try to lift the object the force which I would require would clearly be greater than ($\gt$) $mg$. This means that here the frictional force was applied perpendicular to the surface of contact (if not then why not?) and hence the given definition of friction isn't valid over here. So:
Can we say that in lifting case frictional force is acting?
Why is friction defined this way?
Is there any better definition of friction?