There shouldn't be any difference once the silver is in the water since it will be as ions. As noted in
this MSDS for the mineral cartridge in the Nature
2 system, it is composed of metallic silver, aluminum oxide, and zinc. Presumably the chlorine or non-chlorine shock (MPS) will oxidize both the silver and the zinc into metal ions that get into the water.
The silver chloride in the Spa Frog is a solid that is sparingly soluble but for the small amount that dissolves it will be the same silver ions as produced from oxidation of silver metal from Nature
2.
Because of the presence of chloride ions from sodium (or calcium or magnesium) chloride salt in the initial tap water plus additional chloride added from chlorine, the silver in the water will mostly be soluble silver-chloro metal–ligand complexes as described in
this link. At 10 ppm salt, silver ion is at 111 ppb while the sum of all soluble silver ions and complexes is 209 ppb. At 100 ppm salt it's 11 ppb for silver ion and 121 ppb for that plus complexes. At 1000 ppm salt it's 1 ppb for silver ion and 247 ppb for that plus complexes. So basically the concentration of silver ions in water is somewhat self-limiting due to the presence of chloride from salt. It doesn't really matter whether the source of that silver comes from solid silver oxidized by an oxidizer (chlorine or MPS) or whether it's from dissolving of solid silver chloride.