According to the CDC, here is the definition of vaccine/immunity: https://www.cdc.gov/vaccines/vac-gen/imz-basics.htm

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

> Vaccine: A product that stimulates a person’s immune system to produce immunity to a specific disease

I'm not sure you hit an eventual consistency thing while you read the source you cited, but the definition of a vaccine in it does not match your definition.

A vaccine, according to the CDC source you quoted, is:

> Vaccine: A preparation that is used to stimulate the body’s immune response against diseases. (...)

Keep in mind that your personal definition of a vaccine does not match how most vaccines work, if any vaccine at all.

From the CDC: Vaccine = "Produce immunity". Immunity = "you can be exposed to it without becoming infected" It's right there. This definition, and the most common understanding is that a vaccine means "without being infected".