In this response, I will be using modern terminology to convey my message undestandably to a modern audience, but I do understand that queer history is oftentimes difficult to interpret due to this terminology changing and evolving over time. I also must note that English is not my first language so I apologize for any mistakes in grammar, spelling, etc.

For better understanding of the terminology considering the LGBT+-community specifically, we need to understand the origins of the term homosexual. "Homosexuality" and "heterosexuality" emerged as medical terms in the 1860s, and as a result of the nature of 1800s science they also put these on a hierarchy where heterosexuality was viewed as normal and healthy, whereas homosexuality wasn't. 19th century science primarily created hierarchies between genders, races, sexualities, you name it, and the hierarchy between homosexuality and heterosexuality was one of these hierarchies.

These terms referred first and foremost to men, because women were not really seen as sexual beings. Karl Heinrich Ulrichs was the physician who first invented these terms, but there were many overlapping terms such as "inversion" (Havelock Ellis) and "contrary sexual instinct", which positioned homosexuality as having the sexual instincts of the "opposite sex", so they also kind of conflated being gay and being trans. These texts were written in latin, so they did not bring public attention to the term "homosexual", and this was partly done willingly, as to avoid public attention to content that was deemed too "sexual" for the average person.

Homosexuality was very much seen as something abnormal and the term homosexual specifically carried those connotations. All of these terms were used in sexological conversation up until the 1900s, when "homosexual" started to replace its counterparts. However it still carried heavy medical connotations, and it had been created through a stigmatizing medical gaze. Homosexuality was deemed illegal in many countries, and in addition to that it was also viewed as an illness. The word "homosexual" also excluded women, as was the custom in the sexological and medical field in the 19th and early 20th century.

However at the same time when these terms first emerged, urbanization and industrialization made it possible for clandestine gay subcultures to start emerging as well, when new urban landscapes and modern city culture increasingly provided the anonymity, and hence safety, to participate. So it was only natural in that context that a gay person couldn't really use the word "homosexual" about themselves openly and comfortably, but there was still a rising need to refer to it in some way. So they used other expressions to describe being gay. Gay people themselves referred to same sex relationships as "friendships", or in German "Freundschaft" or "Freundesliebe" ("friend love"). "Gay" in English speaking countries was one term like this, and the first uses of it as specifically meaning homosexual men are from the 19th century. "Gay" had had some connotations of sexual deviancy before, but now it started to refer to homosexual men and sometimes to boys who engaged in sex work with men.

From there on, the use of "gay" started to gradually increase until in the 1960s it replaced the meaning from "happy" to "homosexual male". In the 1960s gay became the primary word which men who were attracted to other men used for themselves. For many decades before that it primarily still meant happy, but the other meaning was still there and so the overlap period was quite long. The word gay also held connotations of frivolity and carelessness, which led to it being associated with camp and showy clothing. Gay still does mean happy or joyous today, but it's defined as the secondary meaning for the word and it's rarely used in that way specifically. So this has turned around during the last hundred or so years.

The 1960s was a decade of new gay activism in many countries, among others the US. This isn't to say it didn't exist before: it most certainly did, quite notably in 1920s Germany, but it can be argued 1960s was the beginning for gay rights activism as we know it today. "Queer" was not a comfortable word for people to use about themselves in the 1960s, because many had bad experiences with it being used as a pejorative. The word "gay", however, hadn't been used in that way, or at least not in the same extent as queer, so it seemed a much more comfortable term for many people to use for themselves. Homosexual on the other hand was perceived as too clinical and medicalized, and at the time homosexuality was still classified as a mental illness in many countries in Europe and in the US, and gay people, especially activists, didn't want to refer to themselves as sick. So the key difference here is that "gay" is a word that gay people pretty much chose themselves to refer to themselves, whereas "homosexual" is actually not. The overlap still kind of exists in the back of our minds, because we still know that it means both happy and homosexual.