Fumed silica is a finely divided silica formed in the vapour state. I think it is used also in clear toothpaste. It is probably listed as silica in the ingredients. Here it probably acts as a disintegrator, ie it prevents agglomeration.I would not use the expression silica aerogel. You cannot have a gel which is also an aerosol, since gels are viscous liquids/solids. You can have foamed gels.

Hope this helps.