@Pete's answers correctly determined what is the salt in the water sample which react with silver nitrate to form the white and brown precipitate respectively. My answer just describe the reactions.
The first one is very much likely to be a chloride salt as it would react with silver nitrate to form silver chloride. Silver chloride has a prominent white color and it is not at all soluble in water.
$$\ce{AgNO3 + Cl- → AgCl + NO3-}$$
It could have been a sulfate salt as silver sulfate is white but is somewhat soluble in water.
The second one is a hydroxide salt.
$$\ce{2AgNO3 + 2OH- → Ag2O + 2NO3^{-} + H2O}$$
Silver oxide is brown in color. It is somewhat soluble in water and actually form dihydroxoargentate ion instead of silver hydroxide.
It is slightly soluble in water due to the formation of the ion
$\ce{[Ag(OH)2]^{−}}$ and possibly related hydrolysis products.
Note that silver hydroxide is not an actual compound. It is just like a solution of silver oxide in water just like ammonium hydroxide(solution of ammonia in water).