Barefoot athletic shoes are typically considered to be those athletic shoes that have the most minimal design attributes and materials which you may as well be running without footwear.
The phrase ‘barefoot running shoes’ is somewhat of an weird phrase as you can not be running barefoot as well as be in running shoes concurrently, unless you count not putting on socks in running footwear to be barefoot within running shoes!
With that in mind, ‘barefoot running shoes’ are "footwear" which are as close as you're able to being barefoot even though still using shoes. Barefoot running shoes have nominal design features and also minimal materials and next to nothing at all for the midsole. They are merely a covering for the foot, most probably to protect the foot from the environment while still enabling the runners being as near to becoming barefoot as you can. Concerning if these footwear in fact reach that goal is obviously open to debate and the scientific evidence is that the running technique in the barefoot running shoes is to some degree different to an authentic barefoot running gait.
Not every barefoot running footwear might be thought of as being “barefoot” or “minimalist” by advocates of barefoot running as many brands and models of these running footwear have a few attributes included such as, for instance, a 5 millimetre stack height for the midsole, which is a lot lower than traditional athletic shoes, however probably not close enough to be regarded as allowing a barefoot running gait. This just shows that over the rather wide selection of running footwear there are extremes in the various design characteristics you can use to match up as to what every individual athlete needs and wants. These array of design characteristics includes the drop (the difference involving the heel to toe thickness of the midsole), the stack height (depth of the sole), flexibleness, and motion control functions (inside density as well as rigid heel counter). On one side with the extremes of each and every of those design characteristics are what could be described as a barefoot running shoe.
As to if you should use or run in barefoot running shoes or otherwise, that is a different issue. They are not without there issues and can take a prolonged duration of adaptation to get used to exercising in them. The promoters of such kinds of running shoes claim that you get less injuries if running using the more minimum running shoes, however, this is not supported with the published research data. Evidence is always that the injury rates in runners wearing more minimalist running shoes is about the same as those who are exercising in the more cushioned running footwear.