Are you talking about sales tax rate or school/real estate tax rate? I'm very familiar with the latter, the former is less common.
Usually when you live in one town but have an address for the city next to it, the town has a different zip code than the city. (That's my circumstance as well.) It is very rare for cities large enough to impose a sales tax to have the same zip codes as communities outside that city's legal boundary.
My mother's house, in a different state, also has a different postal address city/town/village than what is recorded on the property deed, and a different zip code. Neither jurisdiction is large enough to have imposed their own sales tax. They do have different school taxes.