To be fair, it's not just fox, it's plenty of news outlets, medical professionals, etc who have the same opinon. And the CDC did change their definition.
Matter of semantics really. You can compare/contract vaccines all day long. The flu is the one most compared to. I know of no other vaccine that requires a booster every 4-6 months for the unforseeable future. The flue requires a yearly shot. Last time I check, SARS-COV-2 vaccines are relatively new, meaning very little long term data.
How many boosters are you willing to take from a vaccine that hasn't been cleared by the FDA?