The term cottage pie is known to have been in use in 1791, when the potato was being introduced as an edible crop affordable for the poor (cf. "cottage" meaning a modest dwelling for rural workers).
In Argentina, Bolivia, Chile, Nicaragua and Uruguay, a similar dish is called "pastel de papa" (potato pie) or pastel de carne (meat pie). The Chilean version includes minced meat, minced and fried onions, black olives, raisins and hard-boiled eggs.
In the Dominican Republic and Puerto Rico this is called pastelón de papa (potato casserole), it has a layer of potatoes, one or two of meat, and another of potatoes, topped with a layer of cheese. This is called "Yaroa" in Dominican Republic and is usually sweeter than other versions because they either can use potatoes, sweet plantain or yucca.
In Jordan, Syria, Palestine and Lebanon a similar dish is referred to as "Siniyet Batata" (literally meaning a plate of potatoes), or "Kibbet Batata".
In Quebec, a similar dish is called pâté chinois (literally, "Chinese paste"), which contains a layer of corn between the meat and the potato. In English-speaking Canada, the traditional British shepherd's pie prevails.
In Russia, a similar dish is called "Картофельная запеканка" (Kartofel'naya zapekanka, or "potato baked pudding").
In Portugal a similar dish is called "Empadão", with two layers of mashed potatoes and a layer of minced beef in between.