There are two definitions which are used to define electric potential difference:
- The electric potential at position $B$ relative to the electric potential at position $A$ is the work done by an external force in taking unit positive
charge from position $A$ to position $B$.
- The electric potential at position $B$ relative to the electric potential at position $A$ is minus the work done by the field in taking unit positive
charge from position $A$ to position $B$.
These two definitions are equivalent because the external force is equal in magnitude but opposite in direction to the force on the charge due to the field ie $\vec F_{\rm external} + \vec F_{\rm field}=0$ and so the net work done on the unit positive change is zero which in turn means that the kinetic energy of the charge does not change.
With actually stating it to be so the system is the unit positive change and technically both forces, $\vec F_{\rm external}$ and $\vec F_{\rm field}$ are external forces.
In circuit theory if potential rather that potential difference is to be used it is customary to assign one node as the zero of potential and call that the ground or the earth.
Although related another concept is that of electric potential energy and the definition of a difference in electric potential energy relates to the work done by external forces or minus the work done by the electric field in taking the charges from arrangement of charges $C$ to arrangement of charges $D$.
A single charge on its own cannot have electric potential energy that is a property that an assembly of charges has.
Now to try and answer your question.
Assume the system to be a single (positive for simplicity) charge $Q$ which finds itself in an external electric field generated by something outside the system.
The single charge will experience a force due to the field $\vec F_{\rm field}$ and accelerate ie gain kinetic energy due to the work done by the external electric field.
That single charge interacts with the lattice which consists of charged ions and the gain in kinetic energy is balanced by the amount of heat (or other forms of energy eg light in an LED) generated when the kinetic energy is lost.
Where does that heat come from?
It comes from the electric field produced by who knows what.
Rather than talk about forces another way of describing the situation is in terms of electric potential and to say that there has been a decrease in the electric potential of the single charge.
In this case one could say that the work done on the charge by the electric field is $-Q\Delta V$ where $\Delta V$ is the change in the electric potential (the electric potential difference).
Note that in this context you it would be wrong to say that the single charge has lost electric potential energy.
Now consider a charged capacitor.
The capacitor has a stpre of electric potential energy in its electric field and at some time previously something had to do work to separate charges and increase the electric potential energy of the capacitor.
The capacitor also would have a potential difference across its plates.
Consider a system which consists of a charged capacitor whose terminals are connected to resistor.
Positive charge flow from the positive terminal of the capacitor though the resistor and to the negative terminal of the capacitor.
In doing so the electric potential energy of the system is decreased and an equal amount of heat is generated in the resistor.
The amount of charge stored on the capacitor would decrease.
In simple terms you can think of a moving positive charge in the resistor being subjected to the electric field produced by the charges on the capacitor with that electric field doing work on the moving positive charge.
The moving positive charge moves from a position of relative high electric potential to a position of relative low potential and has work done on it in doing so.
Finally consider a "strange" capacitor which has an electrochemical reaction occurring between its plates (terminals).
That electrochemical reaction can move positive charges from the negative terminal to the positive terminal and maintains a constant potential difference across the terminals.
This is a cell in which the chemical energy of the system (battery) is converted into electric potential energy.
Now connect a resistor across the terminals of the cell.
The electric field outside the cell is from the positive terminal to the negative terminal.
Under the influence of this external electric field positive charges will move from the positive terminal through the resistor and arrive at the negative terminal of the cell.
That external electric field does work on the moving positive charge with the result that heat is generated in the resistor.
That moving positive charge has gone from a higher potential to a lower potential and as a result the system (cell & resistor$ has lost some electric potential energy.
However with the cell the moving positive charge moves from the negative terminal to the positive terminal increasing its potential and hence resulting in an increase the electric potential energy of the system.
Overall there is a balance and the electric potential energy of the system stays the same.
After completing a complete circuit the potential of the moving positive charge is unchanged.
Chemical energy has been converted to an equal amount of heat.
Whose work done is the 6V referring to?
In moving a charge $+Q$ from the positive terminal of the cell to the negative terminal of the cell the external electric field generated by the cell does $6\, Q$ units of work on the moving charge, the potential of the moving charge drops by $6\, V$ and $6\,Q$ of heat is generated in the resistor.
In moving the charge $+Q$ from the negative terminal of the cell to the positive terminal of the cell in the opposite direction to the direction of the electric field inside the cell the electrochemical process does $6\,Q$ units of work on the charge and raises its potential by $6\, V$.
If the moving positive charge goes round a complete circuit then its potential does not change, the electrical potential energy of the system does not change, forces acting on the moving charge do work which result in a change of $6\, Q$ units of chemical energy being converted into $6\,Q$ units of heat.
Take your pick.
