Gardisil 9 (Merck) is the only HPV vaccine currently offered in the US. The 9 refers to the fact that it protects against 9 different strains of the HPV virus. In addition to the cancer-causing virus strains (16, 18, 31, 33, 45, 52, 58), it also protects against types 6 and 11, which cause 90% of anogenital warts. The quadrivalent (4 types) version was introduced into clinical practice having completed trials in 2006. The 9 valent version came later.
Historically, vaccines against viral diseases typically used killed or attenuated (weakened) viruses. The Salk and Sabin polio vaccines are examples of these methods. Gardisil is an example of a recombinant vaccine in which the viral surface proteins which stimulate the immune response are made in a yeast or plant vector, harvested, and given to the recipient. This means that there are no intact viral particles, only non-infective surface components, and the vaccine can be made to target multiple viruses.