"This index fund samples the stocks in the index it tracks, relying on statistics to track the index closely. But this other index funds replicates the index; it actually buys every stock in the index, so that it is a perfect copy of the index."
"The scientist tried to repeat so-and-so's experiment, using the same equipment and the same methods, but wasn't able to replicate the results."
"DNA replication is the process by which a cell makes an exact copy of a DNA strand, with the same base-pairs in the same order."
I feel that "duplicate" and "replicate" are synonyms. People claim to see subtle difference in meaning, but I doubt this. I believe that in real life it is simply custom as to which word is used in which context.