Shrimp cocktail is cooked and chilled shrimp served with a tangy dipping sauce. Ceviche is normally raw fish that is "cooked" by being marinated in citrus juices. If you want a cooked ceviche, Mexican Shrimp Ceviche is a great option that is made with red onion, tomato, cucumber, cilantro, avocado, and jalapeño in citrus juices.