The leap forward from the wooden warships to the metal destroyers and cruisers in the 19th century seems gigantic, and the years between them seem so few. Were these types of ships used side by side in the late 1800s, or were the old ships (think Master and Commander) phased out quickly ones the new technology had arrived? Were there any battles where the two were set up against one another?
Yes -- and not well.
The immediate example that comes to mind is the first battle of the ironclad CSS Virginia (ex-USS Merrimack) in March of 1862, when it sailed into Hampton Roads to engage the Union fleet blockading Portsmouth. The Virginia had with it a support squadron, but engaged the Federal ships itself, first firing on then ramming and sinking the USS Cumberland, and then engaging the USS Congress. Congress ran itself onto a sandbar and eventually surrendered after trading cannon fire with the Virginia; after it surrendered and prisoners were being transferred (under a flag of truce), a Union shore battery started firing on the Virginia. The Confederate captain subsequently set Congress on fire using hot shot, then attempted to attack USS Minnesota, which had also run aground trying to escape. However, the Virginia had suffered damage during the battle (her ram stuck in Congress and part of it tore off, and the funnels were shot to pieces, reducing her boiler pressure) and it retired from the action.
The next day, of course, when it was returning to complete the destruction of the US fleet, the Virginia met the USS Monitor in what would be the first (inconclusive) fight between ironclad warships.
Essentially, a fight between an ironclad and a wooden ship was quite unequal -- though the wooden ships were unlikely to be able to sink the ironclad, they could damage it enough to make it eventually retire from the fight (in modern parlance, a "mission kill"). On the other hand, if a Civil War-era ironclad fought with relative impunity, it would be effective mostly inshore or in shallow waters -- once Virginia had its funnels damaged, it became quite a bit slower than the ships it was chasing. The Union monitors, of course, were quite unseaworthy and designed for inshore or brown-water combat.
One of the most celebrated battles in my country was actually beetween and ironclad and a wooden corvette, in the battle of Iquique
in 1879, Peru and Chile were fighting the pacific war, usually called saltpetter or guano war in english, in may 21 the peruvian Ironclad Huascar arrived at their port of Iquique to find two chilean wooden ships blocking it (esmeralda and independecia), the captain tought this was a trap and that the bay was mined, because the ships didnt run, so it kept his distance and hold his fire because the close proximity of the two ships to the port and city (the truth was the esmeralda's engines had broke down so it was unable to flee), the two wooden vessels fired at the ironclad and did basically no damage for an hour, then a second peruvian ironclad arrived and the independecia left south with this new ship chasing it, the esmeralda continue to fire at the huascar with no success, finally realising the bay was not mined the huascar simply rammed the esmeralda and sunk it , with the captain and a few of the crew jumping to board the ship and got gun down.
Now the funny thing is that before this battle the war was really unpopular in Chile, but after the goverment and papers propaganda picture of this little wooden ship fighting for hours and ironclad vessel and never surrendering, his captain and part of his crew even jumping on the enemy ship while it was being rammed, created a huge nationalist sentimient that keep Chile fighting the war until the end, the 21 of may is a national holiday now, and the captain Pratt became a national hero
Chile eventually won the war, and captured the Ironclad Huascar, its a museum now, here a picture, this is actually a sensitive topic in Peru, since the captain of the ship at the time is a national hero, and some polititians want the ship back
Sorry about the many misspellings
Additional to Hampton Roads would be Lissa (1866), where the part-wooden, part-armoured Austrian fleet under Tegethoff defeated a more heavily armoured Italian force. Ultimately, the gunnery available had yet to catch up to armour, and so the combat between the steel ships degenerated into a number of ramming actions. The 'Master and Commander' ships had long been rendered obsolete by steam-powered wooden or iron-hulled vessels like the Nemesis (which fought in the First Opium War in the 1839-42).
Follow up question to the answer of /u/EnclavedMicrostate:
Does anyone have any good information on [Nemesis](https://en.wikipedia.org/wiki/Nemesis_(1839), The British iron warship used in the First Opium War?
I really only know about this ship from the James Clavell book [Tai-Pan](https://en.wikipedia.org/wiki/Tai-Pan_(novel), which while entertaining is maybe not the best historical source.
