English translations of French menus will correctly use both pâté and terrine as pate.
The English word terrine, meaning a cooking or serving dish was taken from the original French at a time when a terrine did not also mean the pate inside a terrine.
There is a short explanation of the meanings behind the single accented pâte, as it may appear on a French menu, at the end of this post.
Pâté de Gibiers - Game pate. The game pate on this menu listing comes from farmed animals. If was part of a hunting season menu, it would be part of a menu called a menu de la chasse. Or, on a regular menu called a pâté de gibiers sauvage, a wild game pate. See the posts on: pheasant,[ii] chamois.[iii] Wild boar,[iv] Rabbit, [v] Quail,[vi] their links are at the end of this post. Game animals may be legally hunted in France, each in its distinct season.
Pâté Forestière – A liver and meat pâté with mushrooms.