Patrice Pavis and Fernando de Toro argue that the term semiology is the correct one, but I keep finding that researchers seems to use both indistinctly.
I would not bother myself with the terminological differences of the kind. Use whatever you prefer. If you need a history of terminological debates for your thesis - that's another question, of course.
Semiology is just one concept of semiotics (de Saussure). It depends which concept you follow and which terms you want to use. If it does make sense to use semiotics in the analysis of theater at all is of course another question.
One approach could appear that adding s comes from SCIENCE: see ECONOMY and ECONOMICS. As a joke, semiology explains better the answer at the question: who was first the EGG or the HEN? The answer is no one, it is a process.( Hoping not to offend someone)
Even if we often consider them as synonyms, there is a difference between "semiology" and "semiotics". The semiology studies the social life of the signs, for example the meaning and the value of the red color (clothes, plastic arts, literature). Semiotics tries to know how the meaning of a text, a behavior or an object builds itself. Semiotics tries to describe the organization of the meaning. One of its bases is the distinction " plan of the expression " / " plan of the contents ".
Any speech, the theater of which, can be the object of a semiotic study.
Of course it is, more than correct, perfectly adequaste to use both concepts, since they complemente acho other. For this manter, YouTube mas find some help reading the text of Ann Überfeldt "Lire le Theatre".
Normally it depends the tradition about you refer : Saussure/sémiologie (and the bibliography that uses Saussure) ; Pierce/semiotics (and the bibliography that uses Peirce).
Saussure inventend the terms sémiologie in linguistics (cf. Cours de Lingustique Générale, 1916, edd. Bally et Sechehaye, but the term appeared the first time in the second edition of the book Adrien Naville, La classification des sciences 1901, but Saussure uses this terminology the first time between 1883-1885, cf. Phonètique and John Joseph 2010).
Searching, I found this new E-book on existential semiotics,"Seen und Schein" by Eero Tarasti. It seems very interesting and had a Chapter called "A proposal for a semiotic theory of performing arts". It is available in english.
A very important question. Recently, in short semiology is considered to be "classical semiotics'. What does this mean?
If semiology studied the life of sings, or was defined as the "science of signs" ( Saussure, (1916), semiotics is now defined as a "cognitive science generating meaning". To my modest opinion, what was once constructed as a linguistically and psychologically based semiotics would be covered with Saussurian, and other structuralism representatives nominations. However, I still hold , as a semiotician, that is is a science of signs. Recently my view is becoming very contestable, and if I may add a sense of humor, one of the reasons why my papers are being rejected.
Notwithstanding this fact, it is also true that we produce meaning. Producing and/or generating meaning to me, does not mean CHANGING it and/or contributing to the various semantic fields changeability. Our aim is not to change meaning, but to reach at the point where various methods, produce meaning. And that should be the place where it stops. It would otherwise risk interpretation. Naturally, please don't take this for granted. As each thesis holds its counter-thesis. When Eco (1994) used to write about the narration process and text analysis, the subtitle of his book was "la cooperazione dei testi narrativi" ( the cooperation of the narrative texts). Somewhere you find "Interpretation" of the text. If one continues in the mentioned fashion, there should not be found any borderline.
However, one thing can be asserted: SEMIOTICS PROPER is what Peirce (1960) used to do. What stands for what? What represents what?
On the other hand semioolgy may respond to questions like: "what can be signified with what", or what is opposed to something else?
John Deely (2009) for instance recently is contesting oppositions. To me rightfully.
In short, it should all belong to philosophy. If the one is ONTHOLOGICALLY based the next is epistemologically.
I have tried to clarify that in my "Semiotics of precision and imprecision" trying to re-group semiotic theories in two big groups, as usual, rejected, and waiting to be reviewed again elsewhere.
Thank You very much for the question. It is really an open discussion among semioticians.
Your question reminds me of another such question about the difference between research methods and research methodology. i will personally disregard the slight difference in semiotics and semiology in theatre studies, as long as both terms refer to study of signs and symbols as indicators of meaning.
let me just bring to notice to this debate that Natyashastra, an Indian treatise on performing arts, too describes physical manifestations of mental states. I have worked during my doctoral studies on these manifestations and one may call them 'signs' in semiotic/semiological contexts. These physical descriptions of mental states are meticulous and detailed about actors' performance of relevant emotion. Though this is in the South Asian (Indian) contexts, I am working towards to test them in 'Western' contexts to see whether 'signs' of bodymind refer to any tradition, society or culture.
By "correct," one ought to mean nothing more than "solves the problems I have." So, if semiology does the work you seek, then by all means use it. It might be wise, however, to embed semiology -- essentially a social science-- in semiotics, which is much broader. One would not want to craft a nice account of theatre, only to find out that one has no way to connect one's findings with what other scientists and scholars are doing/discovering.
There are ought to be a way, for instance, to account for public display and make-believe (in the human realm) in a way that accords with, say the best findings of ethology (bearing on the non-human realm).
That does not mean that humanities scholars have to suddenly become natural scientists, but everyone should keep an eye on the big picture and make provisions for linking up with other fields, at least in principle.
Semiotics (in the Poinsot-Peirce-Sebeok tradition) will let you do that. Semiology won't.
For helpful resources that meet the foregoing desiderata, consultArticle Oxford Bibliographies in Philosophy: Semiotics