Complex systems are always correlated but rarely information processing

`Complex systems are information processors' is a statement that is frequently made. Here we argue for the distinction between information processing -- in the sense of encoding and transmitting a symbolic representation -- and the formation of correlations (pattern formation / self-organisation). The study of both uses tools from information theory, but the purpose is very different in each case: explaining the mechanisms and understanding the purpose or function in the first case, versus data analysis and correlation extraction in the latter. We give examples of both and discuss some open questions. The distinction helps focus research efforts on the relevant questions in each case.