Two vessels have been named Biscayneer, which generally means a sailor or a ship from Biscay:
HMS Leith, also known as HM hired armed ship Leith, was launched in 1744 or 1746 in the British "Plantations", more specifically, the colony of Maryland. From 1764 to 1777 she was a Greenlandman, that is a whaler, in the waters east of Greenland. Between 1777 and 1782 she served the Royal Navy as a transport and hired armed naval ship. She was last listed in 1783.
Ceres was launched at Kolkata in August 1793 as Lutchmy and renamed in 1794. She sailed to England in 1798 and became a West Indiaman. She was condemned at Barbados in 1806. New owners returned her to service, first as a West Indiaman and then as an East Indiaman. She was damaged at Mauritius in 1818 and although she was listed until 1824, it is not clear that she sailed again after the damage she sustained in Mauritius.
Salisbury was built at Havana c.1761 under another name. She first appeared under British ownership in 1781 as a West Indiaman. In 1785 she became the northern whale fishery whaler Rebecca. In 1787 new owners renamed her Harpooner and she was briefly a northern whaler in the Davis Strait. She was wrecked in 1789.
Neptune, was launched in 1805 as a West Indiaman. A French privateer captured her in 1809 but passengers and some disaffected members of the prize crew recaptured her. She returned to the West Indies trade and foundered on 4 February 1825 while returning to Liverpool from New Orleans.
Spy was built in France in 1780, almost surely under another name, and taken in prize. The British East India Company (EIC) purchased her in 1781 and used her for almost two years as a fast packet vessel and cruiser based in St Helena. It then sold her and she became a London-based slave ship, making two voyages carrying slaves from West Africa to the West Indies. She then became a whaler, making seven whaling voyages between 1786 and 1795. She was probably wrecked in August 1795 on a voyage as a government transport.
Tartar was built in France in 1778, almost surely under another name. She was taken in prize and appears under British ownership in 1780. After a short career as a privateer, she made a voyage between 1781 and 1783 as an extra East Indiaman for the British East India Company (EIC). She then became a whaler in the northern whale fishery. After whaling she traded with the Baltic and then served as a London-based transport. She was probably lost in 1799, and was last listed in 1801. If Tartar is the vessel lost in 1799, in 1796 French warships captured her, but the Royal Navy quickly recaptured her.
Two Sisters was launched in 1797 in Nova Scotia and in 1804 shifted her registry to the United Kingdom. A French privateer captured her in 1804 but members of her crew were able to recapture her. She became a coaster and was last listed in 1813.
Traveller was launched at Hull in 1786. She traded between Hull and the Baltic until 1798 or so, when she began maiking annual voyages as a Greenlandman, that is, as a whaler in the northern whale fishery. She was captured in 1808 during the Gunboat War while trading with the Baltic between annual whaling voyages.
Carnatic, launched in 1770, was an East Indiaman belonging to the French East India Company. A British letter of marque captured her in 1778. She became a transport. She was wrecked in 1781.
Mackworth was launched at Neath in 1779. The Admiralty immediately hired her and from June 1779 to March 1783 she served as an armed ship. Between 1783 and 1786 Mackworth traded with the Baltic and the West Indies. In 1786 new owners renamed her Ceres. Ceres was last listed in 1794 with data unchanged since 1791.
Ranger was launched in 1776 in France, possibly as an East Indiaman for the French East India Company, and almost certainly under another name. From 1780 to 1786 she was a British vessel that was a transport and traded generally. In 1786–1787 she made one voyage for the British East India Company (EIC). From 1788 she traded between London and Ostend, and was last listed in 1793 with unchanged data. In 1788 she had sailed to the East Indies, perhaps with new owners from Ostend, and may have remained in the East Indies.
Tartar was built in France in 1779, probably under another name, and taken in prize. She was in 1781 briefly a Bristol-based privateer. A French privateer captured her, but a British privateer recaptured her. She then became the merchantman Friends, and traded between Bristol and North America, primarily Newfoundland. Friends was last listed in 1793.
Biscayneer was a cutter launched in 1779. From at least 1781 on she was a privateer based in Dartmouth, Devon. She captured or recaptured several vessels before her owner-captain sold her in 1783 after the end of the American War of Independence. New owners renamed her Retreat. She was last listed in 1784.
Saville was launched in 1773 in New Jersey, under another name. In 1778 Samuel Enderby purchased a vessel named Rockhampton, which may or may not have been the launch-name, and renamed her Saville. Saville then made four voyages as a whaler in the British southern whale fishery. She returned to England in 1785 and was last listed circa 1787.
Trelawney was launched in 1775 at Liverpool as Clayton, sailing as a West Indiaman. She first appeared as Trelawney in 1779. Between early 1788 and end-1790 she made two voyages as a whaler in the northern whale fishery, and one in the southern whale fishery. She disappeared from the registers between 1794 and 1800. In 1800 she reappeared as a coaster, sailing between the River Tyne and London. In 1809 she started sailing across the North Atlantic to Halifax, Nova Scotia, and Quebec. A United States privateer captured her in 1812.
Trelandvean was a merchant vessel launched in 1767 at Swansea, possibly under another name. Between probably 1777 and 1783 she served the Royal Navy as a ship's tender. She then returned to mercantile service. She may have made on voyage as a whaler in the southern whale fishery, before she was wrecked in the Mediterranean in 1792.
Woolton, was launched at King's Lynn in 1773 as Narr. By 1775 she was sailing between London and Liverpool as Woolton. A French privateer captured and ransomed her in September 1779. In 1781 she sailed briefly as a privateer and made one notable capture that involved a single ship action. After the war Woolton continued to trade primarily between London and Liverpool until she was wrecked in 1785.
Nancy was launched in Newfoundland in 1788. Initially, she traded between Bristol and Newfoundland and then Bristol and Lisbon. After a change in ownership in 1791, she traded between Bristol and Africa. The French captured her in 1794.
Bloom was launched in the Thirteen Colonies in 1781. She was taken in prize in 1782. She became a Liverpool-based slave ship and from 1783 on made four complete voyages in the triangular trade in enslaved people. She was broken up in 1789.
Chaser first appeared under that name in British records in 1786. She had been launched in 1771 at Philadelphia under another name, probably Lord North. Lord North became Cotton Planter, and then Planter, before she became Chaser. Between 1786 and 1790 Chaser made four voyages as a whaler in the British southern whale fishery. She then became a merchantman. In 1794 a privateer captured her but the Spanish recaptured her. She became a Liverpool-based slaver. In 1796 she was condemned in West Africa on her first voyage in the triangular trade before she could embark any enslaved people.