As you pointed out, each state government can enact substantially different tax policies. Note that those are taxes collected in addition to Federal taxes. Federal taxes are typically the majority of what you pay, and those are the same between states.
Since states have wide discretion on state taxes, they often reflect the political goals of those governments. Taxes can be structured to be progressive, or regressive, or to encourage or discourage certain behaviors. Progressive taxation results in wealthier people paying higher rates. Flat taxes and sales taxes tend to be regressive, since for poorer people, these consume a larger fraction of their income. There are also "sin taxes" on things like cigarettes and alcohol, to discourage their use. Similarly, there are often exemptions for things like saving for higher education.
Finally, in addition to Federal and State taxes, many localities, e.g., cities, counties, towns, have their own taxes as well. These are often property taxes on real estate, and are used to pay for local services, like schools, police, and fire departments.