If I earned less than $12,400 in 2020 and use the standard tax deduction, does my tax burden become $0? Would this still apply if my earnings all came from self-employment?

In other words if my total income was under 12.4k but I earned several thousand being self employment still, do I not have to pay any income tax taking a standard deduction? Or...do I only have to pay 15.3% self employment tax and get to skip the personal income burden?