By Thamizhpparithi Maari (Own work) [CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons
No doubt you have seen recipes containing either coriander or cilantro. Usually it's not the same recipe so that might lead you to believe they are complete separate.
It's actually the same thing.
But it's more complicated than that.
Coriander is the name of the plant/herb. Its seeds (or fruit if you prefer) are often used as a dried spice. They are ground and used often in Indian and Mediterranean cuisine, paired with cumin for use in many different types of curries and in garam masala.
It has a flavor of citrus, nuts and sage.
Cilantro refers the name of the leaves of the coriander plant. It looks a bit like Italian flat-leaf parsley, but has a more pungent flavor. It's most often used in Latin American, Asian and Caribbean cuisine.
I've found that you either love or hate cilantro, it's not something that people generally don't care about one way or the other.
Both coriander and cilantro offer its own usage and flavor, but it is a very useful ingredient no matter which part of the plant you use.