Peirce gave several accounts of the ‘triad of interpretants’ and did not always use the same terminology for them. One of the simplest appears in a 1909 letter to Lady Welby, where he compares the Immediate, Dynamical and Final interpretants with three corresponding concepts in her ‘Significs.’ The main difference arises from the fact that Welby is mainly concerned with the meanings expressed in language, while Peirce is more broadly concerned with signs in general, including ‘natural signs’ which are not intended to mean anything.
My Interpretant with its three kinds is supposed by me to be something essentially attaching to anything that acts as a Sign. Now natural Signs and symptoms have no utterer; and consequently have no Meaning, if Meaning be defined as the intention of the utterer. I do not allow myself to speak of the “purposes of the Almighty,” since whatever He might desire is done. Intention seems to me, though I may be mistaken, an interval of time between the desire and the laying of the train by which the desire is to be brought about. But it seems to me that Desire can only belong to a finite creature.
Your ideas of Sense, Meaning, and Signification seem to me to have been obtained through a prodigious sensitiveness of Perception that I cannot rival, while my three grades of Interpretant were worked out by reasoning from the definition of a Sign what sort of thing ought to be noticeable and then searching for its appearance. My Immediate Interpretant is implied in the fact that each Sign must have its own peculiar Interpretability before it gets any Interpreter. My Dynamical Interpretant is that which is experienced in each act of Interpretation and is different in each from that of any other; and the Final lnterpretant is the one Interpretative result to which every Interpreter is destined to come if the Sign is sufficiently considered. The Immediate Interpretant is an abstraction consisting in a Possibility. The Dynamical Interpretant is a single actual event. The Final Interpretant is that toward which the actual tends.SS 111 (1909 March 14)
This clarifies the difference between the “purposes of the Almighty” and ‘that toward which the actual tends’: the tendencies of nature are real but not intentional. Creation is not meant to mean anything.