Cilantro, Coriandrum sativum, describes the first or vegetative stage of the coriander plant's life cycle. The seeds from the same plant are referred to as coriander.
Here in Australia and in the UK, both the seed and the plant go by the one name, coriander.
If you're looking at a recipe which calls for coriander, be sure to check where the recipe is from as it could mean either the herb or the spice. If it calls for cilantro, you can be sure it's the herb or leafy part of the plant.