Is the potential difference between the terminals of a cell in a circuit fixed, or does it depend on the components that are connected in the circuit?
It is fixed.
An ordinary cell delivers power to an electrical circuit. To do this, it must have a certain potential difference across its terminals. The potential difference comes from an electrochemical reaction inside the cell, which proceeds at a fixed rate throughout the cell's life.
Physicists call this potential difference the EMF of the cell. EMF stands for 'electromotive force' - the term is somewhat outdated because it actually refers to a voltage, or potential difference.
The EMF of a cell doesn't change, no matter what other components are connected to it. Even as the cell wears down, its EMF doesn't change. Only if the cell goes "flat" does it lose its EMF.
What does change is the current the cell can deliver. Resistors and other loads limit the amount of current that comes out of it. Also, for a load of a given resistance, the current from the cell decreases over time as it wears down and gains internal resistance.
So the distinction between current and EMF is important - it's the current that changes depending on what you connect to the cell.
To find out more, check out other topics in Electrical Physics!