Dear Hadi Maghsoudiganjeh , fumed silica is produced in a flame or torch, SiO2 molecules coalesce and form silica nanoparticles that aggregate in a chain shaped structure. These "chains" forms a powder that we call fumed silica, with a low density and high surface area.

On the other hand, silica nanoparticles made by sol-gel or other methods are isolated particles. They of course can also form aggregates, but they would be different in shape. Imagine packing roughly oranges (silica NP´s) vs packing bananas (fumed silica) well really they will be more curly and therefore the spaces between them will be larger.

The wiki page shows clearly the process of fabrication of fumed silica:

https://en.wikipedia.org/wiki/Fumed_silica

Another useful, more detailed paper could be this one by

Chapter Fumed Silica ‐ Production, Properties, and Applications

by Herbert Barthel, L. Rösch and Joshua Weis.

Hope it helps.

The difference between fumed silica and sol-gel silica nanoparticle is the synthesis method followed, for instance, fumed silica particles or nanoparticles are synthesized by the thermal pyrolysis method, where silicon tetrachloride (SiCl4) is made to react with oxygen in a flame, and the product SiO2 is obtained where it continuously grows in size or forms aggregates. The sol-gel process is conducted in a liquid phase and the silica nanoparticles are synthesized under acidic or basic catalyst/condition, whereby alcohol solvent(ethanol or methanol) is used to hydrolyze the reactant/precursor silicon alkoxide such tetraethyl orthosilicate (TEOS) or tetramethyl orthosilicate (TMOS). If alkaline/basic condition is used, it is referred to as Stöber method. The concentration of the precursor and catalyst controls the size of the spherical silica nanoparticles.