That is correct for tetanus, flu and a few other vacines that wear out over time. Chicken pox not so much. Hence why you have boosters for tetanus when possibly encountering it and recommended every 10 years as well. Every virus is different obviously or we would have one vaccination for all of them.
Btw tetanus vaccine has way more side effects including high rates of convulsions/seizures in younger children. But of course you would be straight stupid not to get it.