By far the more common word and the one you should use if you are in doubt is “systematic.” It refers to things that are arranged or dealt with according to some system or organized method. “Gerry systematically sorts his socks into piles: those that are still wearable and those that are too smelly.”
Often “systematic” and “systematically” are used metaphorically to imply that something is done so consistently that it almost seems there must be a system behind it: “Tom systematically leaves the toilet seat up.” If you need a synonym for “consistent,” the word you need is “systematic.”
“Systemic” is a much rarer scientific and technical term referring to parts of a body or system. It is frequently used in medicine and biology. A systemic disease affects many parts of the body. A systemic herbicide may be sprayed on the leaves of a weed, but it spreads down to its roots to kill the whole plant. A systemic problem in banking affects many parts of the banking system.
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.”
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