From http://www.iupui.edu/~arisbe/rsources/76DEFS/76defs.HTM

33 - 1906 - S.S. 196 - Letter to Lady Welby (Draft) dated "1906 March 9" .

I use the word "Sign" in the widest sense for any medium for the communication or extension of a Form (or feature). Being medium, it is determined by something, called its Object, and determines something, called its Interpretant or Interpretand. But some distinctions have to be borne in mind in order rightly to understand what is meant by the Object and by the Interpretant. In order that a Form may be extended or communicated, it is necessary that it should have been really embodied in a Subject independently of the communication; and it is necessary that there should be another subject in which the same form is embodied only in consequence of the communication. The Form, (and the Form is the Object of the Sign), as it really determines the former Subject, is quite independent of the sign; yet we may and indeed must say that the object of a sign can be nothing but what that sign represents it to be. Therefore, in order to reconcile these apparently conflicting Truths, it is indispensible to distinguish the immediate object from the dynamical object.

For the moment, let's listen to Umberto Eco's opinion on this: “the immediate object seems to be defi ned as the manner in which the sign circumscribes the way of looking at the object from the point of view of a given sign’s focus (something similar to Frege’s Sinn as opposed to Bedeutung)” (Eco, 1976, p.1462, and from here the discussion is open ...

Reference: Eco, Umberto 1976. Peirce’s notion of interpretant. MLN 91(6): 1457-1472.

As finite creatures with finite means, we are often wrong in our attempts to correctly classify a local region of reality. I may, for instance, think that a distant animal is a cat when in fact it is a dog. In Peircean parlance, the cat wrongly envisioned would be an “immediate” object of my visual signs, whereas the dog “whose characters are true of it independently of whether you or I, or any man, or any number of men think them as being characters of it, or not” would be the “dynamic” object (Essential Peirce, vol. 2, p. 409).

ON THE USE AND ABUSE OF THE IMMEDIATE/DYNAMICAL OBJECT DISTINCTION (JOSEPH RANSDELL):

"In Peircean semeiotic, the immediate object is the semeiotical object as it appears within the semeiosis process as representatively present therein, whereas the dynamical object is the object as it really is regardless of how or what it is represented as being in any given representation of it. The dynamical object is "the thing itself," transcending any given cognition though not beyond cognition generally, whereas the immediate object is the thing as immanent in semeiosis, the thing as it appears to be (is thought to be)."

https://arisbe.sitehost.iu.edu//menu/library/aboutcsp/ransdell/useabuse.htm