This matter in depends on your target and kind of mentioned probiotic.
Some of them would be professional and use for special application for example just using for increase of Growth rate.
Often, some probiotics have multidisciplinary application in aquaculture but some of them has specific application so it would be used just for certain species.
This matter could be considered as immunostimulator (Stimulating the immune system) in specific fish species.
As such there is no problem in using the probiotics isolated from one fish to another. However, it is advisable to use the probiotics from closely related species, so that the chances of success will be greater.