Originally treated as a subversion of the standard gay stereotypes, the Straight Gay is a homosexual male or female character who has no camp mannerisms, Butch Lesbian tendencies, or obviously "gay" affectations.
In the earliest cases, Straight Gays were mostly there for farcical reasons: perhaps as a misunderstanding in which a straight character ends up unwittingly inviting himself out on a "date" with a 'stealthy' gay man, or in which a homophobic character espouses his views to a stranger, only to find out that the person he's talking to is gay. Currently, the Straight Gay is Truth in Television, less of a narrative device than a character type. When still used as a plot point, it may allow other characters to realistically miss that a character is gay, or it may be so incidental to the plot (or controversial as a topic) that it's never actually mentioned on-screen. It's still used for cheap jokes, though.
In some cases — especially Soap Operas — this may be because of the writers changing their minds about an originally heterosexual character.
A lot of gay people object to the term itself (especially with the term Straight-Acting), arguing that gender presentation and sexual orientation are unrelated, and that the term is unnecessarily divisive. Gay men exhibiting masculine tendencies or preferring masculine hobbies isn't necessarily a problem; it's when it is used to vocally differentiate the individual from "those gays" that it becomes an issue. The trope itself isn't necessarily harmful, but applying it to real people can be. Due to these reasons, along with the growing LGBT representation in Western media, the trope is starting to fall into Discredited Trope terrority as such characters have been criticized as making gay or lesbian characters more palatable for straight audiences, especially if they aren't depicted with love interests.
May be associated with Have I Mentioned I Am Gay? in cases where the writing isn't nuanced enough to support a gay character sans constant explanations. Arguably a Spear Counterpart to Lipstick Lesbian, though the "Chapstick" type (not particularly butch or femme) mentioned in its description fits more under this trope. Also compare Armored Closet Gay and The Whitest Black Guy. Manly Gay can overlap with Straight Gay depending on the context, but Manly Gay is more entangled with old stereotypes about gay men. Masculine–Feminine Gay Couple occurs when his lover is more feminine than him.
See also Mistaken for Gay and Camp Straight.