The singular gender-neutral ‘they’ first starts appearing in the 14th century, which makes it a fairly recent innovation in the English language. It is commonly used when the gender of a person being referred to is unknown or irrelevant, as an indefinite pronoun.
Example: Three people are seated In a restaurant. One person leaves momentarily to tidy up. The waiter comes over to collect drink orders; “What will you have?”, and to the second person, “and you?”, and then, gesturing to the third seat, “and do you know what they would like?”
Modern style guides discourage the use of the masculine ‘default’ in pronouns, the old assumption that a generic ‘he’ could be interpreted to refer to any person, masculine to feminine. “Dude” or “guys” often is excused as a slang masculine default applicable to all genders, but it fails a simple test; Try to imagine a couple of dudes sitting in a restaurant. In your minds eye do you see two masculine persons, two feminine persons, or some other combination? The odds are very good that you would imagine two masculine persons.
The use of “they” as a singular definite pronoun, as for non-binary identities, is fairly new, with the recognition of the existence of nonbinary identities. It is a useful tool, however, in acknowledging and affirming nonbinary identities. There isn’t a formal point of introduction that I can identify, just gradual adaptation until it has been recognized as a normal usage by the maintainers of dictionaries. The New Oxford American Dictionary (Third Edition, 2010), calls singular they ‘generally accepted’ with indefinites, and ‘now common but less widely accepted’ with definite nouns, especially in formal contexts.
Cis and Trans are Latinate prefixes, used occasionally as slang forms of cisgender and transgender when discussing gender.
Cis and Trans prefixes originated as Latin prepositions. Cis means “before/within”, “on the near side of”, or “to this side of”. Trans means “across/through”, “on the other side of”, or “other side of”. (Definitions from a dusty old Oxford Latin Dictionary...)
As a prefix Cis and Trans are used similarly; Cistiber, “on this side of the Tiber”, and Transtiber, “on the other side of the Tiber”. They are not exactly opposites, but do often point to opposite sides of some division.
Transgender broadly refers to persons who move away from the gender they were assigned at birth, crossing over one or more of the boundaries constructed by their culture to define and contain that gender.
Cisgender refers to persons not considered to be transgender, persons who have not crossed over any of the boundaries constructed by their culture to define and contain their gender.
Cisgender is not a defamatory term, simply a useful way to identify persons who are not transgender.
Cis and Trans are commonly used colloquially as equivalent adjectives for Cisgender and Transgender.
Caution: I will note that gender critical activists and some others have recently decided to take umbrage at the terms “cis” and “cisgender.” They instead insist on being referred to as “women” and “men”, with transgender women and men relegated to “transwomen” and “transmen” in a nice bit of othering and subtle denial that trans folks are “real”. Some go further and refer to transgender women as “Trans Identified Men”, or TIMs, and transgender men as “Trans Identified Females” or TIFs.
These are deliberately constructed as insults, and derive from some of the hateful content in the book by Janice Raymond, “The Transsexual Empire: The Making of the She-Male”(1979, Beacon Press).