Every area is different. Generally there are rates set by the city / county that apply to various expenses and they get tallied up. Generally based on value with a credit in many areas for seniors, homestead, widow etc.. They add it all up, minus credits and add on any surcharges.
You should be able to look at the bill and see what the differences are to figure out if it is a rate thing, property based on an old value or some kind of non-ad valorem assessment of some kind.
Here there can be swings in tax based on that. Sometimes it is storm water assessments, sometimes city water hookup fees, sometimes the development gets assessed for something because the developer cut a deal with the city to save money and stuck it on homeowners etc. The list really is a mile long and varies a ton.
Every area is different and rates / taxes can vary wildly from county to county or city to city. Even community to community.
Also keep in mind that whatever the property was valued at is likely lower than what you are buying it for. That means the taxes will go up. First year you'll generally pay on the previous record and next will be higher as the city will based the new value on your purchase price. That means if you escrow expect a jump in your payment when that happens. The banks almost never account for that.