Plagiarism is the process of taking another person’s work, ideas, or words, and using them as if they were your own. But I wonder if there is any particular term for the situation in which two people come up with the same original ideas or use the same original words in their own works, neither being aware of the other one's work.
For example, I'm writing an essay on Bernard Shaw, exploring his plays from a particular perspective, unaware of the fact that someone else has already done the same thing.