Answer:
Sodium is placed in group 1 of the periodic table of Alkali metals, and has a valence shell with one electron, making them very reactive. When placed in water, it disperses heat and begins to ignite and burn (due to its very reactive nature), resulting compound is hydrogen gas (H2), and a very strong base (Sodium Hydroxide, NaOH) used for cleaning appliances and for neutralizing agents.
Silver is placed on the transitional metal section of the periodic table, not quite reactive but is the most conductible element on the planet, is malleable and ductile. Due to it being costly and its rarity, it's not relied on for computer parts or wires. Silver doesn't actually directly react with water in its liquid state. It does produce hydrogen gas and Silver Oxide when reacting with water vapour.
In short, Sodium and water create new products, while Silver and water (only in water's gaseous form) form different products.