With ships I'm mainly thinking about warships, but commercial ships aren't necessarily excluded.
My mind can't really think when this change happened: shups made of wood go from ancient times to Middle Ages and more, while iron ships from at least 1900. But between the 18th and the 19th century I have some doubts. I would guess the division is more less in the second half of the 1800's but I'm not sure whether it is a specific point in time or a long process. I'm sure it changes from place to place, that's why I'm focusing in Europe-Mediterranean as my region.
The first warships constructed with significant amounts of iron were a number of floating batteries constructed for the French and British navies during the Crimean War of 1853-1856. They saw little action. The French ships took part in an attack on Kinburn, the last naval action in the Black Sea theatre, while the first two British ships arrived just after this battle was fought. These were wooden ships armoured with iron plates. Flat-bottomed for work in inshore waters, they were largely useless for anything other than shore bombardment. They did, however, demonstrate the possibility of armoured warships.
In 1859, the French launched the first sea-going ironclad warship, the Gloire. Again, she was a wooden-hulled ship with significant armour plating. The British responded with the Warrior, launched in 1860. Warrior had an iron hull, with iron armour over the top of that. Over the next ten years, the RN would build or convert many more ironclads, with 19 in service by 1868. Most of the newly built ships had iron hulls, with ten of these 19 being so constructed. The French were not far behind. The iron-hulled battleship Courronne had been ordered at the same time as Gloire, but would not enter service until 1862, due to delays in the shipyard.
There was something of a transition period that followed. Some ships were built entirely of wood, others largely of iron. The small ironclad Enterprise was made of wood below water, as it would not corrode when sheathed with copper to prevent weeds and algae growing on the hull, but was built of iron above the waterline. Other ships, starting with the 1864 gunboat Vixen, had iron frames, with planks over them. Iron construction would gain in prominence until cheap strong steel started to become available in the 1870s. The first steel-hulled warship was the French Redoutable of 1874, with the British following with the early cruisers Iris and Mercury in 1875. By this time, most new warships were largely built of iron; steel soon gained in prominence. Some ships, especially those that were expected to make long cruises in the distant waters of the Pacific, used the composite methods, with metal frames and wooden planking; this was seen as easier to repair. These designs were still in service through to the turn of the 20th Century.