Which type of chicken to use in a recipe if called for a "hen"?
I suspect what's meant by hen, as opposed to chicken, is a laying hen. When a laying hen's egg production slows down, usually between 3 to 5 years in backyard chicken farming, they're killed and used as 'stewing hens'. Commercial layers are generally culled earlier between 1 to 2 years.

You definitely don't want a Cornish hen. In North America, they're simply whole broilers (usually 7-10 week old birds) - nothing else. Older stewing hens make the best soups, stews and casseroles as the flavour is stronger and the method of moist slower cooking tenderize the tougher meat.