Volt is a name for the unit Joule-per-Coulomb (energy-per-charge).
- 2.5 volt means 2.5 Joules per Coulomb.
- A 2.5 volt battery means that there is a difference of 2.5 Joules per Coulomb from one terminal to the other.
- The actual values (of electric potential) are not known (and are not important); they could be 3 volts at one terminal and 5.5 volts at the other. But the difference in electric potential (voltage) is still 2.5 volts.
The unit of electric potential and of electric potential difference (also called voltage) are the same, namely the volt. A difference $\Delta V=V_2-V_1$ is just a subtraction and doesn't change the units.
how can work/charge express the difference of potentials across the 2 terminals?
Charges want to stay at the point of lowest possible potential. That is thus the low-potential terminal. The battery must do work to move a charge from the low-potential terminal to the high-potential terminal. It must force the charge to move against the repulsion force that the charge experiences from this high-potential terminal.
The work added from the battery is there the energy that turns out to be stored as the charge is finally moved. When the charge then moves (through a circuit) to the other low-potential terminal again, all the stored energy (which equaled the work done by the battery to lift it in the first place) is then spent. The battery must then do work on this charge one more time to again move it to the high-potential terminal.
How can you assign a joule/coulomb value to every point in the circuit?
You can do that just as you can do it to a book on a shelf. It has a certain amount of (gravitational) potential energy assigned to that specific height over the surface.
In the same way, charge is being repelled a lot from the high-potential terminal. The further it moves away from this terminal, the more the potential drops - all other points have other potentials, decreases along the circuit. This is similar to the book falling from the shelf, decreases the (gravitational) potential energy as it falls, since that stored energy is now gradually being "spent" to make it fall. Every point during the falls is associated with another amount of stored potential energy.