What's the difference between similarly rated DC motors with different nominal voltages?
For mechanically similar motors, the difference is the number of turns and the diameter of the wire on the rotor. One motor might use 200 turns of 1 mm2 wire, another wound for half the nominal voltage may use 100 turns of 2 mm2 wire. This means they have the same number of Ampere.Turns when running at the same power. They'll produce exactly the same heat from the rotor.They produce different motors simply for the convenience of being able to run them from different nominal voltages.

However ... Wire is only available in certain sizes, there may not be exactly the 'right' size available for the next voltage. The ratio of copper diameter to insulation thickness will not necessarily remain constant. Thicker wire is difficult to pull tight round the poles, so you may get fewer turns than the ratio suggests than with thinner wire. You can only use an integer number of turns. The air resistance of different wire thickness will be slightly different. All these differences mean there will be subtle, or even not so subtle, differences in the motor performance, especially with motors at the extreme end of the range.

All the motors in the datasheet have nominally the same speed, torque and power, with the exception of the torque of the 6 V motor, which is lower. Maybe this is due to the thicker wire meaning fewer turns on the rotor?

While the mechanical, rotor, heat are all nominally the same, the commutator will be running at a high current in the lower voltage motors. This may mean they need uprated or wider brushes, or that the brushes and sliding contacts don't last as long. The commutator in the higher voltage motor is subject to a higher voltage, as the rotor has a higher inductance. This may mean they need bigger gaps, or higher resistance brushes, or that the edges of the commutator don't last as long.