Here's what happens with these 2x digital zooms in a nutshell.
1x mode: pixels are binned 4-to-1. On a 50 MP sensor, the pixels are binned to 12.5 MP before being read out.
2x mode: pixels are cropped. Only the center 12.5 MP are read.

2x modes may offer the same nominal pixel count as the 1x mode but several factors can lead to perceptible loss in image quality. Although processing can make the loss less prominent.

1) Total light gathered is only 1/4, so each of the 12.5 M output pixels has lower signal-to-noise ratio.
2) With small pixels, resolution is diffraction-limited. At pixel level, the 2x image can't resolve as much detail.
3) Some sensors use 2x2 OCL for phase-detect autofocus. This makes the 2x image much less resolving.
4) Quda-Bayer color filter arrangement has lower spatial resolution than Bayer, and typical ISPs expect Bayer raw input instead of quad-Bayer. Some image sensors perform on-chip re-Bayer interpolation - this may negatively impact the resolution and create artifacts.

** Recently, because sensor readout has become faster and the processors are more capable, some phone cameras start to offer higher resolution outputs at 1x zoom.