Generally speaking, vaccines can be split up into 4 different categories. Keep in mind that although there are 4 different types of vaccines, the overall intention is to create a strong immune response in the person receiving the vaccine.
Live or Attenuated Vaccines
Live, attenuated vaccines are, as the name implies, alive. Virulent/sickness inducing components of the pathogens are removed to prevent the vaccine from harming the receiving individual. These types of vaccines produce stronger, longer lasting immune responses compared to other variants.
Inactivated or Killed Vaccines
Inactivated or killed vaccines utilize dead specimens to elicit an immune response. These types of vaccines produce a weaker immune response and generally require booster shots.
Recombinant Vaccines
Recombinant vaccines use pieces of a pathogen to produce an immune response. Like killed vaccines, these are weaker and generally require multiple series for adequate protection.
Toxoid Vaccines
Some infections, like diphtheria and tetanus, are due to toxins that a pathogen creates. Toxoid vaccines utilize small amounts of these toxins to elicit an immune response. These typically require ongoing booster shots to protect individuals.
Source
1. U.S. Department of Health & Human Services. Vaccine Types. https://www.vaccines.gov/basics/types. Updated March 2020. Accessed April 22, 2020.