Thanks for taking the time, nicely explained.A "barefoot shoe" is simply a style of footwear that attempts to mimic, as closely as practical, the concept and feel of wearing no shoes while still providing protection for the wearer's feet. Usually that involves having no heel raise (which most shoes have nowadays) and no arch support (also very common), and the thickness of the sole is generally minimised to maximise "ground feel", which helps the muscles in the foot (and leg) develop and strengthen when walking, running etc.
Of course, the thickness of such footwear can vary since an extremely thin sole may not always be sufficient for activities like trail running, which could require a sole with better grip and perhaps more protection against small rocks and that sort of thing, but it depends on the experience of the wearer (some very experienced trail runners can run in those huarache sandals that are only 2-3mm thick without any issues).
They typically have a wider toe box than standard shoes as well, which is designed to help the feet and toes spread normally without being "forced into" the shape of the shoe, like so:
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Aesthetically speaking it can make for unusual looking foorwear sometimes but some brands do it well without making them look goofy.