the Roman tax: money a subject people owed the emperor, charged on persons and property rather than on goods in transit
This is a Latin word in Greek dress. Rome called the assessment of a province, and the tax rolls it produced, the "census," and Greek speakers simply borrowed the term. In the Gospels it no longer means the paperwork but the money: the tax a conquered people owed the emperor. Only Matthew and Mark use it, and its foreign sound carried its own message, since this was Rome's own word for Rome's own demand.
Two things separate it from the other tax words of the New Testament. It was charged directly on people and on what they owned, rather than skimmed off goods in transit, which is the work of the toll word (τέλος). And it was Rome's tax, not the temple's: the yearly due Jewish men paid for the sanctuary was a different payment with a different name (δίδραχμος). Luke tells the same tribute story using the ordinary Greek word for tribute (φόρος), most likely because his Greek was smoother and his readers sat further from a Roman tax office, not because he meant a different tax.
Most scholars identify this tax with the yearly charge Rome laid on each person in Judea once it became a province in 6 CE, the levy that provoked the revolt of Judas the Galilean. That history is why the question put to Jesus, whether it was lawful to pay it, was a trap and not a technical query: saying yes insulted a crowd who remembered that revolt, and saying no handed Rome a charge of stirring up rebellion. A minority of scholars read the word more narrowly, as the registering and valuing of property behind such taxes (ἀπογραφή is the word the New Testament uses for that registration), and doubt that any charge per head existed in Judea this early.