Need help understanding Federal and State Quarterly payments for self-employment (private contract). Am I paying 15.3% for each? What about social security and Medicaid?

So I understand that I owe 15% federal plus social security and Medicaid which currently estimates to 23% I think. But then I read somewhere else that income tax has to be added in addition to that? Then what about Maryland state tax? All I can find is the number 15.3% and the Maryland Gov. website is calculating me closer to 7% even though I marked 0 employer withholding.