I believe you are describing a charge pump.
You don't give any specifics on what you're trying to do, though, so I can't really give meaningful feedback on anything else. Generally speaking, though:
I am looking to capture as much energy as possible from a small steam turbine using a DC motor and then use that to power another DC motor.
If you're driving it, it's a generator. Not all DC motors are the same, so you can't just grab any DC motor and spin the output shaft and expect to get voltage at the terminals. Shunt motors, brushless motors, etc. will require extra inputs to get a useful output.
Essentially my idea was to charge a capacitor using the first dc motor until a specific voltage and then discharge it as fast as possible into the other dc motor.
You don't get to pick how fast a capacitor discharges unless you can control the load resistance/impedance. The motor will determine how quickly the capacitor discharges. And again, you haven't stated anything about the drive cycle, supply/consumption voltages, etc., so I'm not clear why you're not just driving the motor directly with the steam generator.
Also as a secondary question what would be the advantages and disadvantages of using a battery vs a capacitor in this situation?
Capacity/energy density, but also inherent voltage regulation. Battery voltages are determined by their chemistries; a fully discharged lead-acid battery may still read about 10.8 volts. A capacitor still has a charge at 1 V, but that may not be useful energy because the voltage isn't in a useful band.
Don't re-invent the wheel. Don't re-invent the switching mode converter. If you need to change the bus voltage, use a buck/boost converter to a voltage that is suitable for your output, and then use a battery float if you need surge capacity (where the instantaneous power demand might be greater than the source can generate, even if your source is capable of delivering >= the average power demands.)