It is allowing you the state download at no cost. You may able able to paper file the state return for free. You would be charged $20 for e-filing the state return.
The filing deadline is probably similar to the federal and e-filing the return is quicker to file, quicker to process, and quicker to get a refund.
The state return generally will use the federal return amounts in calculating the state tax return. Many state returns start with the federal agi. By preparing the state return in TurboTax like you did the federal return assures you that the same federal numbers are carried to the state returns and they match.
The IRS and state tax departments share information from the returns you file with both of them. So they should match.
