First, this is the anti-vax shill who wrote that false argument:

https://en.wikipedia.org/wiki/Joseph_Mercola

If anyone bothers to checks it, they get:

Early CDC definitions about vaccine "that stimulates a person’s immune system to produce immunity":

https://web.archive.org/web/20210826113846/https://www.cdc.gov/vaccines/vac-gen/imz-basics.htm

Note that the entire phrase is important. The vaccine 'stimulates a person's immune system' as the aim is generally to produce imunity; it's not a guarantee of immunity. So this is a matter of basic reading comprehension, which anti-vaxxers can conveniently overlook with the excuse that they were home schooled or whatever.

Secondly, some of those footnote links no longer work and one has to go to the new CDC page to see what changed:

https://www.cdc.gov/vaccines/glossary/index.html#heading-v

Vaccine - A suspension of live (usually attenuated) or inactivated microorganisms (e.g., bacteria or viruses), fractions of the agent, or genetic material of the administered to induce immunity and prevent infectious diseases and their sequelae. Some vaccines contain highly defined antigens (e.g., the polysaccharide of Haemophilus influenzae type b or the surface antigen of hepatitis B); others have antigens that are complex or incompletely defined (e.g.Bordetella pertussisantigens or live attenuated viruses).

The key phrase for the anti-vax readers is: "administered to induce immunity and prevent infectious diseases and their sequelae." Hence the attempt in this case is induce immunity or prevent infectious deseases, but again it's of course not a guarantee of anything. And the language is so similar as not to imply anything actually changed.