How do image sensors output in different resolutions?
Depends on the sensor type, but I believe it's generally just the whole sensor, resampled after readout.  "Digital zoom", on the other hand, is the way to say 'crop' in marketing speak.  For many high speed video cameras, they can read out a small portion of the sensor at a higher frame rate than they can read out the whole sensor so at the high end of the frame rates supported, there is generally a tradeoff between frame rate and resolution with an approximately constant value of 'pixels per second'.  There are some really fancy sensors that have multiple sets of readout electronics that can read out pixels in groups for better low light performance and less processing overhead at a lower resolution.