What is the difference between “rooster” vs. “cock” and “hen” vs. “chicken”?

Since cock is American slang for male genitalia, it’s fallen out of use in America (not in England!) except when specifically referring to cock fighting. Chicken is genderless, hen is the female, rooster. cock and cockerel are male, and chick refers to the younglings (of either sex).

There is no difference between rooster and cock. "Cock" is also known as "rooster". An adult female chicken is known as "Hen".

Cock is short for cockerel. When a cockerel is part of a group of hens (roost) to encourage egg laying, it's called a rooster. I'd say rooster is more common in American English and cockerel (cock) is British English.

Edit: Here in Vietnam, cocks are sometimes pets like dogs. I see Vietnamese take their cocks to the park or the riverside. They may spar them, not full on cock fights (though this may be more common than seen) so they are really cocks not roosters, as they lack a roost.

“Cock” is the Old English word for the male domestic fowl, and it is still the common word here in Britain. “Rooster” is basically a prudish euphemism, rare in this country, but it has become the usual word for this fowl in North America. “Cock” as a colloquial word for the male genitalia is as common here as it is in America. It is just that we are not too squeamish to use the same word in two meanings.

"Chicken" includes both sexes. "Cock" is (as mentioned) the male. "Hen" is the female. "Chick" is the baby of either sex.