Natural and Barefoot are different things,
Natural Running is simply running in a zero drop shoe, anything from the 4mm sole of the Vibrams to the 10mm of shoes like some Saucony/Asics.
Barefoot is either running barefoot or running in a shoe with very limited padding on the sole, Vibram, Vivo etc
You’ll always be best moving to a zero drop shoe with cushioning before a barefoot shoe. It helps develop your muscles and is more forgiving.