The terms: Cornish, CornishX, Cornish Game, Cornish Hen, Game Hen, Cornish Game Hen, and Jumbo Cornish Rock Cross are used so interchangeably on these forums perhaps i can offer some clarity.
Cornish: An APA and others clubs, recognized breed in both standard and bantam sizes. Tracing it lineage back to crosses between Indian Asils and Old English Games. (A failed attempt at breeding a bulldogish pit fowl. Really, look it up.) AKA: Indian Game, Cornish Game
CornishX: A hybrid of mysterious lineage. It is more than just a White Rock crossed with a Cornish. The modern commercial meat bird.
Cornish Game: 1.Used in reference to the Cornwall area tradition of gambling, blood sports and the breeding of animals for the pit. 2. A breed of chicken who heritage can be traced to Cornwall.
Cornish Hen: 1. A female older than a year of Cornish breeding. 2. A small and wide meat chicken of either male or female gender. Usually processed at a young age. 3: A single serving whole bird meal presentation of chicken.
Game Hen: A hen of game-fowl breeding.
Cornish Game Hen: 1.Can be used in the reference to any female of the Cornish breed. 2. Cornish Hen Definitions 2 & 3.
Jumbo Cornish Rock Cross: The CornishX under another name with "Jumbo" added for marketing reasons.