Well no, a fem character with a dick is variously called an otoko no ko, a shemale, or a trap, depending on how offensive you want to be about it. Futanari is from a Japanese word for "two" and means having both.
There's literally a Wikipedia page; you don't have to take my word for it.
Nobody really uses it to mean that anymore. Back in the day, like early 2000, then yes, basically all futanari was exclusively with both pussy and cock, and like 90% of the time without balls. However as the genre exploded in later years, it became overwhelmingly just a female character but you swapped out the genitals. Having both, especially without the balls as more classical futanari would, is pretty rare nowadays
So why not use "shemale", as it would be more correct in a technical sense? Because futanari is tightly associated with 2D or 3D rendered content, so for people who are looking for that type of content specifically it is convenient to have that tag on porn websites. Search futanari on rule34 or something and you will see that overwhelmingly, this is the colloquial usage. Much bigger than, say, genderswap. Or any of the others you mentioned. So if you want to find a female character you like from some anime or whatever in this style, the way to find what you'd referr to as "shemale" for her would be to add "futanari" tag
Otoko no ko and trap are also different, and those characters, while effeminate, are still distinctly male. Sometimes in porn they will give otoko no ko some slight hint of boobs, but that is in the same way as they will do that with uke characters in yaoi. Otoko no ko is more leaning in towards shotacon, and "trap" is a very old term that hardly is used anymore. "Trap" is still in the same vein, but it is mostly referencing IRL young males crossdressing erotically, not 2D. This is also from mid 2000s to early 2010s. You'd see this a lot at 4chan at that time, and it was a lot of those traps who ended up giving birth to the modern transgender movement after a pretty substantial amount of them decided to go on with hormone therapy and stuff. Bailey Jay (a.k.a. Line Trap) being the most influential figure, as she had started transitioning even earlier and was sort of a frontrunner