when electrons drift in a metal from lower to higher potential .does it mean that all the free electros of the metal are moving in the same direction

No, it doesn't mean that all the free electrons of the metal are moving in the same direction.

 

When a potential difference is applied across a metal, the electrons gets accelerated towards the positive potential. The velocity of electrons increases but it happens so only for a short time. It is because of the fact that the electron experiences a random forces due to vibrating ions in the metal. Therefore, the electron may get deflected or scattered in a wide range of directions due to the action of random forces.