I would call "imitation" a coin struck following the model of another coin, at the same weight and finesse, with identical or very similar pictures and script. The goal of these coins was not to deceive, but to gain acceptance on the "market" by exploiting similarity with other well-known and well-valued pieces, thus providing a profit to the minting authority, but not necessarily an illegal one. This was definitely common practice in the Middle Ages and the Venetian ducat was certainly among the most imitated currencies, not only in the Eastern Mediterranean but also, for instance, in Rome.
I would call "contemporary counterfeit
" a coin struck as above, but with reduced weight and/or finesse, compared to the original type. The goal of these coins was definitely to deceive, i.e. to gain an illegal profit, again by exploiting similarity with other well-known and well-valued pieces, but this time spending the currency at a face value higher than it real value ("intrinsic" value, i.e. its precious metal content). This practice became extremely common in the late Middle Ages down to the 17th c., in many small feudal mints of Northern and Central Italy for example.
Of course, the border between the two cases is very blurred. As far as I know, your Chios ducat is considered an imitation, at least in its early stages, as its weight and finesse were identical or very similar to the prototye.
Hope this helps