THOSE who campaign for Britain's becoming a republic would not be understood by a citizen of ancient Rome, though he would easily recognise the word. "Nonne," one can hear him say in his best Latin, "haven't you got one already?"
The Latin res, often translated "thing", had a lot of meanings. One of them was "situation"; another "affairs", another "the State", which is what res publica meant, the publica being added to distinguish this sort of res from other sorts. The Romans were pretty certain they lived in a republic, despite being ruled by a hereditary emperor - just as the French, having seen off the Bourbons, thought nothing odd about going on calling their country la republique francaise while living under the dynasty of Napoleon I.
Res could also be property or wealth, so res publica turns exactly into "commonwealth"; this was how Ralph Robinson in 1552 translated the respublica (one word by then) of the Latin in which Thomas More wrote his Utopia. Sometimes Robinson makes it "the common wealth", sometimes "the common weal". More's never-never land featured no monarch, but kinglessness was not, I think, what respublica principally meant to him. Francis Bacon was among the first to use the word republic meaning specifically a state with an elected head, and to muse on its advantages. For honest Tom Paine it was obvious that true democracy required the fall of the House of Hanover.
Since then republic, like democratic, has been borrowed by revolutionary dictatorships with the idea that the people can be fooled by a bit of doublethink. But this is an old game. Cromwell had already fooled them into believing he had established what he called a "Commonwealth" by abolishing the monarchy, then taking powers indistinguishable from those of a monarch.