Lessening symptoms is not the definition of a vaccine even by the cdc’s own page.
It PREVENTS YOU from geting the disease and being infected in the first place.
Here from their page discussing vaccine terms:
Definition of Terms
Let’s start by defining several basic terms:
Immunity: Protection from an infectious disease. If you are immune to a disease, you can be exposed to it without becoming infected.
Vaccine: A product that stimulates a person’s immune system to produce immunity to a specific disease, protecting the person from that disease. Vaccines are usually administered through needle injections, but can also be administered by mouth or sprayed into the nose.
Vaccination: The act of introducing a vaccine into the body to produce immunity to a specific disease.
Immunization: A process by which a person becomes protected against a disease through vaccination. This term is often used interchangeably with vaccination or inoculation.
https://www.cdc.gov/vaccines/vac-gen/imz-basics.htm
Note they do not mention natural immunity at all, however. Deliberately omitted.