What is the difference between US notes and silver certificates?

Silver certificates were bills backed by silver on deposit with the Treasury. They could be issued only in quantities that didn't exceed the total value of that silver. At one time, when the price of silver was fixed by the government, it was possible to exchange these bills for silver bullion as well as coins. When the price of silver was deregulated in the mid-1960s silver certificates were discontinued and the practice of exchanging for metal was ended. Most silver certificates are recognizable by their blue seals.

US Notes were currency issued directly by the Federal Government (rather than through the central bank) but not backed by gold or silver on deposit. Most of these had red seals and serial numbers. They were issued from 1862 to 1966, and were discontinued only as a money-saving move to consolidate all currency production and administration under the Federal Reserve.

Federal Reserve Notes (green seals) are the only kind of currency now printed in the US. They're produced by the Bureau of Engraving and Printing* for each of the 12 districts administered by the Federal Reserve system, the nation's central bank. Like US Notes, they're not backed by any gold or silver but instead rely on the stability of the government to validate their acceptance in the marketplace.

(*) Regardless of common myths and misunderstandings, only the BEP makes bills. The US Mint is responsible for coins and is totally separate from the BEP.