Zeroed (Thevenin) - the standard in circuit theory. Any linear circuit seen from two terminals behaves like a single voltage source UAB with a series resistor RAB (Thevenin’s theorem; equivalently a current source with a parallel resistor - Norton’s theorem). To find RAB the sources are turned off: an ideal voltage source keeps its voltage at any current, so for changes in current it acts as a short (0 Ω). An ideal current source keeps its current at any voltage, so it acts as an open circuit.
This mode answers questions about behaviour under load: how much a divider’s voltage drops when a load is connected (U = UAB · Rload / (RAB + Rload)), what current flows when A-B is shorted (UAB / RAB), which load gets the most power (Rload = RAB). When a voltage source sits directly between A and B the result is 0 Ω - an ideal source has no internal resistance. A real source (battery, power supply) does: draw it as a resistor in series with the source.
Removed - the resistance of the resistor network alone, as if the sources were pulled out of the board, leaving empty spots. This is what an ohmmeter between A and B shows with the power disconnected. Useful when the source is on the schematic only incidentally and you care about the ladder, divider or bridge itself, or when checking an ohmmeter reading. Note: removing a voltage source cuts the branch it was in, so the result can be very different from Thevenin mode.
In a circuit without sources both modes give the same result. Node voltages, currents and power on the schematic are always computed for the full circuit with sources - the switch changes only RAB.