Its interesting that you mention probiotics, with vitamins in the same context.
Although probiotic for humans might mean a food such a yogurt with bacteria such as acidophilus, that enter the digestive system .
For aquarium, the term probiotics often refers to the use of beneficial bacteria in the system itself, as opposed to food.
In aquarium lingo, a probiotic bacteria is one that competes with pathogenic bacteria for dominance in the filtration system, the substrate or other general areas.
It may mean a product like Rid-X that inoculates the system with populations of non pathogenic bacteria, to basically edge out the ones become infectious to our fish,
These can be very beneficial to the system, some like rotifers consume waste and metabolism by-products, thereby preventing the pathogens a place to live, and raising water quality. They can also use up substances that prevent an organismm like cyanobacteria from getting a foothold.