Does the electron in wire too move because of voltage difference? When we talk about electricity through a circuit because of a battery it is said that the electrons from negative terminal travel to positive terminal of the battery.
I can't help but imagine about the free electrons in that wire, does the electrons of negative terminal repel them and in that way we say the electron move towards positive terminal? OR the electrons in the negative terminal itself only(with no involvement of wire electrons) moves towards positive terminal?
This might also answer my other question which is: does electrons move in an electric circuit like water moves in a pipe or the electrons of wire just repel and displace from their position?
 A: 
I can't help but imagine about the free electrons in that wire, does
the electrons of negative terminal repel them and in that way we say
the electron move towards positive terminal?

The electric current is the movement of free electrons in response to the application of an electric field by the battery. The electric field applies a force to the free electrons making them move from the negative to positive terminal.

does electrons move in an electric circuit like water moves in a pipe
or the electrons of wire just repel and displace from their position?

Water moves in a pipe in response to a pressure difference (mechanical force). You can think of that as analogous to electrons moving in a circuit due to a voltage difference. If you shut a valve in the pipe, flow stops. But if a pump is still running there is still a pressure difference as evidenced by a pressure gauge reading. You can think of the battery as analogous to the pump. If you open a switch in the electrical circuit current ceases, but there is still a voltage difference (electrical potential) across the battery terminals as evidenced by a voltmeter reading.
Hope this helps.
