Ship building was an interesting industry, with the rise of mathematics and engineering design, steam power and international trade Europe saw an explosion of ship designs and hull types. The 'mathematical' method involved thousands of calculations and took almost 9 months to design a ship - which was a very good ship, mind you but that meant there was far too long between tow projects. The traditional method was to experiement and tweak existing successes through trial and error until you ended up with a good ship.

The two main distinguishing feature in the Age of Sail were the way they were rigged and the how the hull was contructed. Two main types of ship contruction were used, a clincker type which was popular in Northern Europe involved long overlapping planks fastened onto the superstructure. A Viking long ship, for example, were always constructed this way. Alternatively, you could chose to save material by not overlapping your planks such that it forms a smooth continuous surface - this was the caravel style and more popular in the Mediterrean (esp by the Portugese and Spanish).

More importantly, a ship was classified as to what type of sail she carried. There are many types of rigging, and each have their own pros and cons. Northern and Western Europe were primarily square rigged ships making them much faster top speed by sacrifices the handiness of lanteen rigged ships that was able to tack into the wind with much less difficulty. This website has a lot of say about the different rig types, sometimes they are classed by tonnage and sometimes they are classed by the amount of sail they could carry.

You will note that most warships will be square rigged, as the main sails can be reefed (taken up) to give better visibility on the fighting deck with the top-sails set to still give them ability to sail. A lanteen sail rigged ship will have almost everything obscured by the boom (which is also dangerous as if swings from side to side).

By the advent of the Napoleonic Wars, British ship building programme has very advanced and still produced warships of a very sturdy nature owing to the wide bottomed design, giving them a very stable fighing platform. This was taken onboard as a design from the Dutch, of whom many were employed. As the sounds of the Netherland were quite shallow, a flatter and rounder bottom was called for to reduce draught but this made them a little slower in the open sea. In contrast, French ships had a much narrower profile (ie not a tub) that cut through to water and very fast speeds. Coupled with the fact that their maritime doctorine consisted of blockade running and piracy, they specialised in building frigates which darted in and out of Brittany, Brest and Marseilles to attack mechant convoys. The Americans had a very strong ship building programme, their ships were very strong and much sought after. They 'tradmarked' the American Sloop of War, a small handy vessel that packed quite a punch! They also sailed to Australia, supporting the newly found colony of New South Wales with rum and other sundry goods (but mainly rum).

Please downvote until I can find my source, at work right now