Self employed people pay both the employer and employee taxes. They pay Federal income taxes.  They may have to pay for their own medical insurance.  They may have to pay income taxes on the cost of transportation provided as income,  as many pay income tax on company cars provided and per diem if provided. A self-employed person/individual contractor owes payroll taxes which cover Social Security and Medicare.  It's called Self-Employment tax.   12.4% tax for Social Security and  2.9% tax for Medicare.
 If they have taxable income of  $80,000, their Self-Employment tax would be $12,240.