I don't think there is any such thing (yet) as hepatitis C shots, if by "shots" you mean a vaccine. The scientists are trying, but so far no effective vaccine for Hep C has been developed or licensed by the FDA. Hep A and B do have vaccines available.
Hep A, B, and C are unrelated viruses that all infect the liver. Hep A is sometimes called Infectious Hepatitis because it is spread through contaminated water or through contact with someone suffering from Hep A. Hep A is common in parts of Asia, so it is routine to get Hep A shots before visiting China.
Hep B and C are both so-called "blood viruses" that are spread by contact with the blood or other bodily fluids of infected people (similar to the ways in which HIV is spread). Both Hep B and C can develop into chronic infections which damage the liver over time and can lead to cirrhosis and even liver cancer. Hep C chronic infection is more common than Hep B.
The good news is that modern medicine has recently developed some miracle drug cures in pill form for chronic Hep C infection: Solvaldi, Harvoni, and others. The bad news is that these drugs are frightfully expensive. But they are still much cheaper than getting a liver transplant to replace a liver destroyed by decades of chronic infection.
The older treatment prior to these drugs involved getting interferon shots - perhaps these are the Hep C shots you are referring to. But the interferon therapy had dreadful side effects and isn't used as much any more if the new drugs are available.