Drachmas are Greek coins (or weights more precisely) and the sources for each of these two stories are originally written in Greek. Shakespeare used a translation of Plutarch's lives, composed in Greek, and the gospels including Matthew were also composed in Greek.

The four drachma coin that Matthew writes about Peter pulling out of the Fish's mouth and paying two sets of two-drachma temple taxes with is thought to be a Tyrian Shekel

In Plutarch's Life of Caesar, nearly all monetary values are given in drachmas, while Suetonius's Latin composed account of the same events gives all monetary values in sestertii and doesn't mention drachmas.

Shakespeare's source for Caesar's life was Plutarch, who had recently been translated into English at the time of the writing of the Julius Caesar. Plutarch was a Greek writing in Greek, and as is common with Greek writers in the Roman Period he converts all weights and measures to his more familiar Attic standards. In the life of Antony Plutarch mentions that Octavian demanded the money from Caesar's fortune, which Antony was withholding from him, so that he might execute as Caesar's heir the clause of Caesar's will that provided 75 drachmas to every citizen. A Roman author would've given the price probably not in denarii (which is really pretty rarely used by our texts) but in sesterces--Augustus in the Res Gestae boasted of paying each citizen 300 sesterces according to the provisions of Caesar's will. Likewise, the New Testament was written in Greek in a part of the world where Greek was the language of literature and business.