The US corporate maximum tax rate is 35%. What does this mean for US corporate taxes especially in regard to the different state tax rates?

First of all, you have to differentiate between state
taxes and federal taxes.  The state taxes are paid to the state governments.  The
federal taxes are paid to the federal government.  Of course, it's all the same to the
company as they are still having the money taken away.  But the two taxes go to
different levels of the government.  So a company in California would pay a bit less
than 9% of its taxable income to the state of California and another chunk of its
taxable income to the US government.

Now, as far as what
that 35% rate means, there are a number of things you need to
realize.

• That rate does not apply to all
  companies or to all of the income of any company.  The US tax rates are progressive.  A
  company with up to $50,000 in taxable income pays 15% of that to the federal government.
  


• A company making $75,000 in taxable income is in the 25%
  bracket but does not pay 25% of its whole taxable income.  Instead, it pays 15% of its
  first $50,000 and then 25% of the next $25,000.  This is because the tax rates are
  marginal tax rates.


• The
  firm's taxable income is not the same thing as its total income.  Firms, like people,
  get to take tax deductions for various things.  The tax is
  only paid on the taxable income, not the gross
  income.

So, the 35% rate means that the
companies that make the most money pay 35% of whatever they make over $18.3 million. 
They do not simply pay 35% of their gross income or even 35% of their taxable income. 
Instead, their tax is determined by multiplying various amounts of their income by the
marginal rates for that portion of their income.  Please follow the link that ends
"federal tax rates" to see exactly what the rates are on which portions of the firms'
incomes.