A transformer has a Voltage and a Current rating. In your case the call out is for a transformer that produces a steady 12VDC and capable of at least 100ma in one case and 500 ma in the other.
If you tried to run the 500ma set up on the 100ma transformer you would be trying to pull more current then the device is rated for and it would overheat and fail.
If you chose a 1000ma device you have a reserve of capacity and will run below the rating. But you not as efficient either. So it is a balance.
Think Train transformers, it is similar. G
Just to add what G says and this applies mainly to unregulated wall warts. The nominal voltage is only close at rated current. Most wall warts are unregulated. They put out as much as 1/3 more voltage below their rated current. Probably not much of in issue for a static grass circuit but can be for other voltage sensitive devices like Miller Signs DC-DC convertors.
Use a 12V 500ma wall wart for something that requires 10ma and it will likely never get below 15 volts.
The alternative is make sure you have a regulated wall wart. They will be marked such. In that case the voltage will stay close to the rated voltage regardless of current draw.
