MSAA does indeed have a higher information capacity, since the MSAA output surface has a 2x, 4x or 8x higher resolution than the rendering resolution, it's not a 'software post-processing filter' like FXAA or SMAA.

The output of a single pixel shader invocation is duplicated 2, 4 or 8 times and written to the MSAA surface through a triangle-edge coverage mask, and once rendering to the MSAA surface has finished, a 'resolve operation' happens which downscale-filters the MSAA surface to the rendering resolution.

SSAA (super-sampling AA) is simply rendering to a higher resolution image which is then downscaled to the display resolution, e.g. MSAA invokes the pixel shader once per 'pixel' (yielding multiple coverage-masked samples) and SSAA once per 'sample'.