Semeiotic is a term used by Charles Sanders Peirce to distinguish his theory of triadic sign relations from other approaches to the same subject matter, more generally referred to as semiotics.
There are three principal ways that a sign can denote its objects. These are usually described as kinds, species, or types of signs, but it is important to recognize that these are not ontological species, that is, they are not mutually exclusive features of description, since the same thing can be a sign in several different ways.
Beginning very roughly, the three main ways of being a sign can be described as follows:
An index is a sign that denotes its objects by virtue of an existential connection that it has with its objects.
A symbol is a sign that denotes its objects solely by virtue of the fact that it is interpreted to do so.
One of Peirce's early delineations of the three types of signs is still quite useful as a first approach to understanding their differences and their relationships to each other:
The second kind of representations are such as are set up by a convention of men or a decree of God. Such are tallies, proper names, &c. The peculiarity of these conventional signs is that they represent no character of their objects. Likenesses denote nothing in particular; conventional signs connote nothing in particular.
The third and last kind of representations are symbols or general representations. They connote attributes and so connote them as to determine what they denote. To this class belong all words and all conceptions. Most combinations of words are also symbols. A proposition, an argument, even a whole book may be, and should be, a single symbol. (Peirce 1866, "Lowell Lecture 7", CE 1, 467-468).
Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857-1866, Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1982. Cited as CE 1.
Peirce, C.S. (1865), "On the Logic of Science", Harvard University Lectures, CE 1, 161-302.
Peirce, C.S. (1866), "The Logic of Science, or, Induction and Hypothesis", Lowell Institute Lectures, CE 1, 357-504.
Awbrey, Jon, and Awbrey, Susan (1995), "Interpretation as Action : The Risk of Inquiry", Inquiry : Critical Thinking Across the Disciplines 15, 40-52. Eprint.