The virus is SARS-CoV-2, the disease it often triggers is Covid19. Its like HIV and AIDS.
The vaccines prepare the body for exposure to the virus to minimize the disease response and lowering the potential shedding of the virus to others. Getting vaccinated has little to no immediate effect. It takes weeks for the immune response to produce adequate antibodies to have protection from the disease response. Vaccines that require 2 stages stretch that time out to weeks longer.
https://www.verywellhealth.com/covid-19-vaccine-immunity-time-5091651