Just as the title suggests, was the term for the renaissance years coined and used during those years, or is it a modern word used retrospectively?
Sort of. The Italian artist and critic Giorgio Vasari (1511–1574), who wrote The Lives of the Artists, used the term "rinascita", which has similar connotations. However, the term "Renaissance" proper was a later invention according to the book "The Renaissance" written by Paul Johnson.
The term "Renaissance" was first prominently used by the French historian Jules Michelet in 1858, and it was set in bronze two years later by Jacob Burckhardt when he published his great book The Civilization of the Renaissance in Italy. The usage stuck because it turned out to be a convenient way of describing the period of transition between the medieval epoch, when Europe was "Christendom," and the beginning of the modern age.