A battery behaves somewhat like an ideal voltage source. That is, it will maintain a reasonably constant voltage between its terminals over some range of current.
A battery (or other power supply) that is rated "12V, 200A" does not force 200A to flow in a circuit. It forces 12V across the circuit, and the circuit will draw however many amperes it wants from the battery when 12V is forced upon it. The "200A" rating of your battery means that if the current drawn by the circuit is 200A or less, then nothing bad will happen.
If a fan or a piano or any other device that uses electric power is rated "12V, 2A" then that usually means that it needs 12V in order to function correctly and, it will not draw any more than 2A when it is functioning correctly.
Beware the word "usually!" Most electronic devices expect a constant-voltage power supply, and most power supplies are designed to supply a constant voltage.
Some applications (e.g., high power light emitting diode lamps, arc welding) need a regulated current, and some power supplies are designed to adjust their voltage output as needed in order to force a certain current through the circuit. These types of power supply usually will be labelled for a very specific application, and you won't see the typical howevermany volts at somenumberof amps rating.