Augustine distinguishes natural and given signs. The first signify with no intention of signifying, while the latter signify because a person has an intention to signify. The distinction, at least in part, is a distinction of will.
Peirce’s typology of icon, sign, and symbol depends on a different criterion. Peirce is looking at the relation of the signifier to the thing signified, rather than to the intention of the communicator.
Augustine and Peirce are (perhaps) not disagreeing with each other in their analysis of signs so much as attending to different features of signs.
