What is the difference between a 12V and 24V DC motor?
On their respective power supplies both motors should perform identically but the 12V motor would draw twice as much current from its 12V supply compared to the 24V motor on a 24V supply.

In other words power supplied to both motors should be quite similar for a given mechanical load. Mechanical load power is defined as \$2\pi n T\$ where n is speed in revs per second and T is torque is newton-metres. And if the 12V motor took 4 Amps to supply a certain mechanical power output then the 24V motor would take 2A to perform identically.

DC motors of the simple type (trying not to generalize here) will rotate at full speed on no-load and this speed is mainly determined by the applied voltage. Putting 24V on a 12V motor may wreck it. Conversely, on heavy loads, the speed normally reduces fairly linearly with torque but on a 24V supply there may be enough potential for the motor to fry due to it being able to supply more torque and speed. Don't do it is my advice.