The two words are both centuries old, so have had many chances for various authors and fields to adopt them for differing purposes, sometimes in contradictory ways. So for example a "complex system" (in the sense of the Santa Fe Institute) means something moderately different than what Tim Peters means. In plain English, they are broadly synonymous, so if you were writing a newspaper story you shouldn't expect readers to find subtle differences between them.

But if you know somewhat what implication a particular writer intends in drawing a distinction between the two words, then there's no inherent problem. "Simple is better than complex. Complex is better than complicated." is a pithy way to express a valuable idea:

We should try to make our interfaces, data structures, implementations, systems, etc. "simple", that is, dealing with just one thing at a time, in a clear and straightforward way, with few components each with a well defined purpose, etc. Sometimes, however, there is inherent difficulty in a problem or in the world requiring many interacting pieces, but we should still aim to avoid making things "complicated", that is, tangled, messy, difficult to reason about, ambiguous, unpredictable, gratuitously mixing unrelated concerns, etc.