The 18th century was a time during which the great powers of the world were still developing into "modern" armies , and did not yet have models/patterns of swords for the most part. These would would become implemented towards the end of the 18th century. As a result, prior to the adoption of regulation pattern of swords, there was a great deal of flexibility in allowance for what a given officer, crewman, ship might have available, and a greater variety in designs than would be seen in the later 19th century.

While there were many nations and many ships across the world during this time, the world powers vying for control of the high seas during the 1700s were primarily the British, French, and Dutch. If you are investigating the arms used by navies, especially via portraits/paintings, you will find an overrepresentation from these nations during that time period.

In general, the types of swords found on ships were slightly shorter than those used by soldiers on land. The crowded space found on naval vessels (either below decks, or with the mass of equipment on the deck) favors a side arm with a slightly shorter blade. The lack of cavalry warfare also minimizes the need for swords over 32" in length.

The types of swords could go by several names; in British English usually they would have been called Cutlass or Cuttoe and looked something like a shorter version of an infantry sabre; typically curved (some are straight), single edged, with a hilt with varying degrees of hand protection.

The word hanger is also used, although this is often reserved for a cutlass style sword, which is then used on land. However the terms are to some degree interchangeable depending on the writer and the time.

As this was the time of the Golden Age of Piracy it is worth noting that pirates were even less discriminating about what types of swords they would carry than those found aboard military vessels. Pirates would have no qualms carrying a gentleman's small-sword, or even older rapier, if they wanted to show off their opulence and appear aggrandized.

Ships from the Morrocan, Ottoman, and Zanzibari coasts might favor types of Nimcha, as a shorter sabres than those found inland.

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Futher east during the sailors of the Qing might have carried full length swords; various types of Chinese Dao and shield.

https://3.bp.blogspot.com/-JOS5zecJZRg/VZfdyl_8n-I/AAAAAAAAA1U/GCc_raTn460/s1600/fuchuan.png

As a bonus, here as another post that showcases some of the swords that may have been seen on Royal Navy, Dutch Navy, and French Navy vessels during the 1700s.

https://www.reddit.com/r/SWORDS/comments/ivtrv7/avast_in_honor_of_a_international_talk_like_a/