Sorry, I wrote my comment early in the morning and I didn't explain myself clearly.
"Coriander" was the standard English word, and "cilantro" the standard Spanish word, way before the European arrival to the Americas.
My understanding is that American English got the word "cilantro" for the leaves from Mexican cuisine... and then Mexican Spanish did the opposite and took the word "coriandro" for the seeds from English, to differentiate between the leaves and the seeds. I don't know how common the word is though; I have never been to Mexico so don't take my word for it.
However, European English and Spanish still use just one word each. If you ask me, I will say "hojas de cilantro" (leaves) and "semillas de cilantro" (seeds). It is not so common in our cuisine, so there is no need to have different words.
However, I have seen the opposite situation, Mexican people calling the seeds "coriandro", probably due to USA influence.