It does depend on the type of sensor, the comment above was close but a bit incomplete/imprecise. Many modern sensors use a technique called binning where the final image's pixels are calculated by combining a 2x2 grid of sensor pixels via some signal processing, halving resolution in both dimensions but improving sensitivity and allowing for many DSP-based capabilities; whether they are actual improvements over the raw image is implementation-dependent and partially subjective. When shooting at 2x digital zoom though, you bypass the binning and use the sensor pixels directly, resulting in an image with the same "true" (non-upscaled) resolution as a 1x shot, minus the signal processing. Any other digital zoom, whether between 1x and 2x or above, is indeed a crop of a larger image.

It is a clear step above cropping a 16mp sensor to 2mp for zoom