If a toroidal power supply transformer says for example "15-0-15V 1A" on its label does that mean it's 1 amp for each rail, or 1 amp for total 30 volt output when not using the split? I looked online but couldn't find a definitive answer to this. Thanks.
You are talking about 'rails' which makes me think this is a transformer-rectifier-filter capacitor question.
If you build an audio amplifier supply using that centre-tapped transformer and four diodes (or a bridge) and a filter capacitor you will get about +/-20V.
The maximum DC current you can safely draw is 620mA from +20 to -20 (25W).
If you use two diodes and a filter capacitor you will get a single rail of about 20VDC at 1A maximum (20W).
The transformer rating itself is based on a resistive load and is 1A RMS for the total winding (30VAC) so 30VA. When the currents from each end of the winding are equal, the center tap current is zero. If you use only 1/2 the winding you should not exceed 1A, so in that case you would only be able to get 15VA from the transformer.
In practice you could probably get a bit more because the heating from the second half of the winding is not there, but not a lot since copper heating rises with the square of current. 18VA might be safe. Maximum DC current from a rectifier/capacitor will be commensurately less.