Capacitors in parallel all sit between the same two wires, so the voltage across every one of them is the same.
With the voltage the same, the charge follows and is proportional to the capacitance. Twice the capacitance holds twice the charge, and in the figure that is twice as many field lines.
The total charge is , so seen as one capacitor the capacitance is . Wiring in parallel is the same thing as widening the plates, and the capacitance grows accordingly.
With capacitors in series, the conductor between one stage and the next is joined to nothing else. No charge enters it from outside and none leaves.
So every stage carries the same amount of charge. With the charge equal, the voltage follows and is inversely proportional to the capacitance. That is why the smaller capacitance takes the larger share of the voltage.
The total voltage is the sum over the stages, . Seen as one capacitor, , and the combined capacitance is smaller than any single stage.
To see why the charge is shared in series, take out just the conductor between two stages. It is the lower plate of the upper stage joined to the upper plate of the lower one.
Because it is joined to nothing else, the total charge on that conductor is zero from beginning to end. If is drawn onto its upper plate, then is all that can be left on its lower one.
That is how appears on the next stage too. This is the reason the charge is common in series, and it holds whatever the capacitances are and however many stages there are.
Batteries in series add their electromotive forces. Put identical cells in a row and , so the voltage you can put across the capacitor rises with them.
Batteries in parallel leave the electromotive force at that of a single cell. What grows is the current they can supply, and the share carried by each cell drops to .
It is the mirror image of capacitors. Capacitors gain capacitance in parallel; batteries gain voltage in series. Both come down to whether one voltage is being shared or several are being stacked.