Electrons do not generally move in one direction unless in the presence of an electric field and even then their motion is only accelerated in the direction of the field.
At room temperature, the electrons move simply due to the thermal energy they possess. And this is random motion NOT in one general direction
However, due to the chemical reaction occurring within the battery, a potential difference is set up across its terminals. In practicality, if a wire is connected between the two terminals, at any two points on the wire there is some potential difference due to the fact that the wire is non-ideal and has some finite resistance due to which there is a potential drop between any two points.