The adjective systematic means (1) carried out using step-by-step procedures, or (2) of, characterized, or constituting a system. It typically describes carefully planned processes that unfold gradually. Systemic, which is narrower in definition, means systemwide or deeply engrained in the system. It usually describes habits or processes that are difficult to reverse because they are built into a system.
There is some gray area between the words. When there is doubt, it’s usually safer to go with systematic, which is older and more broadly defined.
But Shia say they suffer systematic job discrimination at the hands of the ruling minority, who are Sunni. [NPR]
They carried out a systematic review of previous research to examine the association between infrequent physical and sexual activity and acute cardiac events such as heart attack. [Irish Times]
The hackneyed old complaints about systemic bias against women no longer seem convincing. [Globe and Mail]
Post-weaning multi-systemic wasting syndrome (PMWS) does not affect humans but attacks young pigs … [New Zealand Herald]