These two words, both adjectives, are closely related, but different in meaning.
Systemic means “a property of a system (as a whole)”:
Systemic racism is difficult to avoid and even hard to detect in any society consisting of marganlized racial groups.
Anxiety seems to be a systemic problem in the human body.
The first example, systemic racism, is the most common phrase using this word. It means discrimination that arises from the structure of the system, such as the way “the rich get richer and the poor get poorer”—another systemic problem. Systemic racism does not depend on racist people—it is “baked in” to the system, as we say.
In the second example, systemic means that the anxiety does not belong to a single organ or body part, but rather affects the whole body.
Systematic, on the other hand, describes any pattern (anything not random)—i.e. anything that embodies a system (of rules):
Bob put away his clothes using a systematic method: alphabetical order.
Alice did her job systematically, step-by-step, keeping everything in order.
Systematic often describes behavior, but it can describe other patterns:
It is obvious that the stars are not arranged systematically.
Science began when a person first noticed systematic patterns in nature.
In other words, systematic means “regular, predictable, or ordered.”