I added what I thought was dissolved table salt into silver nitrate and a precipitate formed. Is this salt?

From what I know, a precipitate forms when there is a change in solubility. If you added NaCl to water, then immersed this solution in AgNO3, then you do not necessarily have to get NaCl back. Because there is water in the solution, I would ume that you have some insoluble silver compound instead (probably AgCl because it is a double replacement reaction).