I just recently became aware of Korea's Admiral Yi and the "Turtle Ship" he and his navy employed. I was wondering if there were any other examples of ships so unique?
There was a great deal of difference in designs of ships among navies in the Age of Sail, but nothing would stay unique for long. The often-cited example is the difference between the English and Spanish fleets at the time of the Armada -- broadly speaking, the English ships were built longer, lower, and more weatherly, and employed different tactics from the Spanish galleons. The English fleet was able to harass the Armada, break up its cohesion, and prevent the Spanish ships from being effective fighting machines, and eventually chase them up the Channel and out of reach of Parma's army in the Netherlands (which was the goal of the Armada -- to ferry Parma across the Channel).
But in general, advances in shipbuilding would be studied and copied by other nations -- the French and Spanish, for example, liked hiring English/British and Irish expats as shipbuilders, preferably those who had had experience in English building yards. As a single example, the frigate type of ship originated in the Low Countries (specifically, as a ship used by Dunkirker privateers in the last half of the 17th century), then was copied by the French and English.
Here are some older comments I've written about ship construction, if they're of interest:
https://www.reddit.com/r/AskHistorians/comments/20x9kz/classes_of_vessels_during_the_age_of_sail/
https://www.reddit.com/r/AskHistorians/comments/2709jm/how_would_a_britishhms_frigate_built_in_1715/
Now there were certainly types of ships that you'd find in certain areas -- the xebec comes to mind as a Mediterranean ship, as do galleys that were used there even up through the 1800s -- but at least in Western Europe, shipbuilding was a craft that tended to converge.
If you have follow up questions about any of the above, let me know!