What is the difference between a chicken and a hen?

A hen is an adult female chicken, chicken is the general term for the bird (can be male or female).

Chicken is the breed.
Hen refers to the sex of the bird.

Male chickens are known as roosters (in the U.S., Canada and Australia), cocks, or cockerels. Castrated roosters are called capons.
Female chickens are known as hens, or 'chooks' in Australian English. Young females are known as pullets. Roosters can usually be differentiated from hens by their striking plumage, marked by long flowing tails and bright pointed feathers on their necks.

https://en.wikipedia.org/wiki/Chicken#General_biology_and_habitat

We call all of them chickens when we seen them in a flock. We call the females hens and the males roosters.

The trail on this cursor is too cool.

All Hens (in this context) are Chickens, but not all Chickens are Hens!

This thread brings to mind a Seinfeld episode:

Frank Costanza: Let me understand, you got the hen, the chicken and the rooster. The rooster goes with the chicken. So, who's having sex with the hen?

George Costanza: Why don't we talk about it another time.

Frank Costanza: But you see my point here? You only hear of a hen, a rooster and a chicken. Something's missing!

Mrs. Ross: Something's missing all right.

Mr. Ross: They're all chickens. The rooster has sex with all of them.

Frank Costanza: That's perverse.

http://www.imdb.com/title/tt0697769/quotes