If you got your flu shots you could say that you got your vaccination, your immunization or your inoculation
and you would be correct with all three words. However the words do have different yet overlapping meanings.
Vaccination is the act of administering a vaccine. Although the word "vaccine" started with Jenner's cow pox it was expanded by Pasteur to mean all inoculations intended to perform immunity. The vaccine is a pathogen or toxin rendered survivable either by altering it or, most commonly, by using minimal amounts.
Immunization is any part of the process of becoming immune, but particularly the part taking place within your body as a response to a vaccine. You could gain immunity without a vaccine, and you could get a vaccination without gaining immunity.
Inoculation is a wider term for any transfer of tiny amounts of a material to a living organism, but the word has expanded beyond biology and is used in varied ways. An inoculation does not need to be for the purpose of immunization although immunizing is the most common usage. Intentionally infecting a lab mouse with a disease is inoculation but not intended to immunize. The original use of the word was to graft seeds (also called "eyes" thus the "ocula" etymology) which has nothing to do with immunity.
In some medical circles, inoculation is skin administered, while vaccine is oral or both oral and skin, but there is no such concise definition by universal agreement.