The resulting binaural DSD recording approximates what a listener would hear at a performance of the music if they were sitting at that spot using an audio principle known as HRTF (Head Related Transfer Function). So, the only difference between stereo and binaural recordings is the microphone setup used. The intended result are recordings optimised for either spaced loudspeakers or headphones. For stereo recordings, the primary microphones are two mics typically spaced four to eight feet apart, matching the spacing of most home loudspeaker placements.
Ways of recording
Binaural recordings are made with two microphones implanted into the ears of a head shaped model known as a "dummy head" (see for example the Neumann KU-100 Binaural Microphone system)
Playing a binaural recording on a stereo setup
While binaural recordings are specifically intended for headphones, and will not reproduce the same in standard speaker setups (due to crosstalk of left speaker reaching one's right ear, etc) it is in no way damaging to hear the recordings on a stereo setup.
Spatial Audio
Spatial audio is different from Binaural. We're specifying 2ch Binaural as a recording captured with a physical binaural microphone head during production (above), and 2ch Spatial as a derived 2 channel deliverable optimised for headphone reproduction, created in post production. Read more about Spatial Audio here.