Cunt is a woman-only insult in the US (and very strong, but Americans are, on the whole, more sensitive to swearing), but I feel like in other English-speaking countries it's more commonly used to refer to men.
I generally find swear words a very interesting area linguistically (in Spanish too there are some countries where words are very offensive, and others where they're a regular part of daily conversation).
Coño isn't really cunt though, despite its literal meaning - you can't call someone a coño, you'd use it for emphasis like we'd use fucking. Mothers will even say it to young children when they're exasperated, which is wild if you're translating literally ("hurry up, you cunt" to a 4-year-old is hard to imagine even in Australia).
Similarly, puta isn't bitch, it's whore, and it's incredibly difficult to define bitch accurately to Spanish or Portuguese speakers - there are words that are somewhat similar, but no perfect fit. And literally everyone has been told that bitch means prostitute, so they have to unlearn that first...plus it's super offensive to call someone a puta but less offensive as an adjective, again akin to fucking in English: when faced with a bowl of slop you might say "Pero por qué no has cocinado bién las putas cebollas?" (but why didn't you cook the fucking onions properly?)
All a bit off topic, but trying to translate and teach swear words is actually a really difficult and delicate part of linguistics. I find it fascinating, but it can take a lot of work!