Often I come across the term "female author" rather than "authoress". Which is the correct usage? "Female author" sounds wrong to me as other words that end in "-or" take a sex.
Learn English – Should I use “authoress” for a feminine author
grammatical-gender
Related Solutions
As a personal opinion, I'll suggest that there is no tidy single word term for gender specific words. In fact "gender-specific" or non-gender-specific or similar are probably as good as you can get.
No noun is immune to gender differentiation, or removal of gender differentiation. If somebody takes a term that is usually asexual and produces two new gender based variants that are recognisable, it will probably not survive, but there is no reason why an especially apposite creation may not become part of the language. Some words may have a general and eg female version but no distinctly male equivalent. eg the (contrived for the purposes of this illustration) term "pilotess" would be immediately understandable. I cannot think of a distinct male equivalent. [For female-er-ising, addition of "-ess" works in many cases ! :-) ].
Such choices either way, as have occurred in 'recent times', are liable to have been driven by the desire on the one hand to use gender inclusive language, and on the other hand to use terminology which makes a point about discrimination or differentiation when it is used.
The term dancer is indeed gender inclusive, but "ballerina" exists as a term which overwhelmingly suggests a female protagonist. The term "male ballerina" gives 14,000 Google hits - but most seem to be asking what the correct term is (Some suggest "Cavalier"). Some sites such as this one are so bold as to use the term directly , but still manage to revert to the occasional "male ballet dancers" indicating that the usage is unusual.
The suffix " ...ina" tends to suggest either 'small' or 'female' but this is not necessarily so in all cases.
For added fun, consider the gender inclusive / male only / female only versions of: Waiter, Host, Bellboy, Pointsman (cars), Point-man (guns), Aviator, Dominatrix, Seamstress, Druid, Governor, Best man, Minx, Cougar, Priest, Nun.
Many need extra discussion to explain variants. eg "Dominator" may be the proper male version of Dominatrix but loses a certain something. Priest may become priestess, but not always. Seamstress seems to have no equal. etc
"Ladies and gentlemen" is a phatic expression, that is:
communication which serves a social function, such as social pleasantries that don't seek or offer any information of value.
If you're going to cut hairs on even that phrase, then you should be saying
Ladies and gentlemen and boys and girls and teen and preteens and elders and babies and deceased and conceived and...
But we all have things to do with our lives. So we just say "ladies and gentlemen." (Now, people who don't have things to do might wonder about that expression and why it isn't more "inclusive," but I digress...)
As to the context of your question, if it were on a train, the announcer could simply say, "Attention passengers."
Boom, done. Next.
Best Answer
The term exists but it's considered "old-fashioned, sexist and patronising", as it says in my dictionary (NOAD):
If you want a further reference also the OALD says the same thing.