While their general function is the same, the types of bacteria used are very different. This is because there are many different kinds of bacteria and each thrive in different environments. The environment of the gut is very different from the environment of the skin.
Probiotics in the form of yogurt or supplements target the gut biome. The types of bacteria need to be able to withstand more acidic environments. Though these products also aim to shift the balance of good and bad bacteria, they would not be suitable for the skin, and vice-versa.
The AO+ mist uses a bacteria suited for the skin: Nitrosomonas - a family of bacteria that consume ammonia found in our sweat, in turn producing beneficial byproducts that lead to healthier looking skin.