No, shrimp ceviche and shrimp cocktail are not the same thing.  Ceviche is shrimp that has cured in lime juice. The rest of the ingredients can vary by region or taste.  Shrimp Cocktail, on the other hand, is made with boiled shrimp and always served with a side of cocktail sauce made of ketchup, chili sauce, prepared horseradish, fresh lemon juice, Worcestershire sauce, and hot sauce.