Inulin is a polysaccharide, while FOS is an oligosaccharide.
In short, each is yet another "not-quite-sugar carbohydrate" touted for supposed advantages vs. yeast infections. Problem is, most studies of any saccharide seem to compare it against SUCROSE, instead of against a no-carb diet, so any and all benefits may actually just come from cutting sucrose, while adding the FOS/inulin/xylitol to a no-carb diet could actually be counter-productive.