Illegal means prohibited by law. Illicit means prohibited by societal custom. Since laws usually emanate from societal customs, what is illegal is usually also illicit. But since societies typically do not enshrine all of their customs into law, what is illicit may be completely legal.
Consider the example sentence in the graphic above. The writer of this sentence correctly distinguishes between the related but different meanings of illegal and illicit. While the behavior (whatever it was) violated a societal custom, the prosecutor determined that no laws had been violated and thus the behavior was not illegal. What is illegal is often illicit, but what is illicit may not be illegal.
Make sure that your writing recognizes such subtle differences in language. More precise language makes for more effective writing, and that better communicates the image of yourself and your brands that you want to convey to your audience.