Systemic means system-wide or deeply engrained in the system. The term “systemic” is often used in medicine and biology. A systemic disease affects many parts of the body. A systemic problem in a business affects many parts of the business such as operations, finance, human resource, products, or services.
Systematic means carrying out using step-by-step procedures or organized methods. The term “systematic” typically describes carefully planned processes that unfold gradually. It implies that something is done so consistently that it almost seems there must be a system behind it.
If you’re talking about how something is done according to a system, the word you want is “systematic.”
If you’re talking about something happening to or inside of a system, the word you want is “systemic.”