My first thought was that this was an either/or question: it could only be France or the USA. But in fact, the only country that Britain was fighting in the 1790s was France. This was the time of the French Revolutionary Wars, when (to paraphrase Wikipedia) France was opposed by Great Britain, Austria, Prussia, Russia and "several other monarchies." Even the United States was fighting France in the years 1798 to 1800, in what Wikipedia calls the "Quasi–War".
The French Revolutionary Wars ended in 1802 when Britain, finding itself fighting France alone after its allies fell by the wayside, agreed to the Treaty of Amiens. But (to quote Wikipedia again), "the lingering tensions proved too difficult to contain", and the Napoleonic Wars began just over a year later.
Tory Island is off the coast of County Donegal, in the north west of Ireland. The battle that was fought near to it on 12 October 1798 was the last action of the Irish Rebellion of 1798 – led by Theobald Wolfe Tone – which Wikipedia describes as "part of the Atlantic Revolutions [beginning with the American War of Independence, and continuing at least into the 1870s] and the French Revolutionary Wars".
The Battle of Tory Island resulted in a decisive British victory, and ended the final attempt by the French Navy to land substantial numbers of soldiers in Ireland. Wolfe Tone was captured three weeks later at Letterkenny, in Donegal, and died in unclear circumstances on 19 November 1798 (some five weeks after the battle).
The word 'Tory' – tóraidhe in Gaelic – is variously translated as 'bandit' or 'pursuer'. It was used in the Irish Confederate Wars – contemporaneous with the English Civil War, to which they were related – to refer to irregular fighters on the Irish Confederate side. Meanwhile, a radical faction of the Scottish Covenanters (who sought to maintain the Presbyterian doctrine and polity as the sole form of religion of their country) formed themselves into the Kirk Party, which supported the future Charles II and crowned him as King of Scotland in 1651. The Scottish opponents of the Kirk Party disparagingly nicknamed its members 'whiggamores' or 'whigs' – a term most likely originating (according to Wikipedia) from the Scots for 'mare drivers'.
In the years 1679 to 1681, attempts were made in the English parliament to exclude the Catholic heir presumptive James, Duke of York, from the thrones of England, Scotland and Ireland. Those who supported the Exclusion Bills became known as Whigs, and the supporters of James's claim became known as Tories – associating each of them with the radicals and rebels of a generation earlier.
This early incarnation of the Tory Party ceased to exist as an organised political entity in the early 1760s, although it was used as a term of self–description by some political writers. A few decades later, a new Tory party would rise to establish a hold on government between 1783 and 1830, with William Pitt the Younger followed by Robert Jenkinson, 2nd Earl of Liverpool.
Wikipedia explains how the modern Conservative Party came about, and came to be known colloquially as the Tories:
"The Earl of Liverpool was succeeded by fellow Tory Arthur Wellesley, 1st Duke of Wellington. His term included the Catholic Emancipation, which occurred mostly due to the election of Daniel O'Connell as a Catholic MP from Ireland. When the Whigs subsequently regained control, the Representation of the People Act 1832 removed the rotten boroughs, many of which were controlled by Tories. In the following general election, the Tory ranks were reduced to 180 MPs. The Tamworth Manifesto, issued under the leadership of Robert Peel, began to transform the Tories into the Conservative Party. However, Peel lost many of his supporters by repealing the Corn Laws, causing the party to break apart. One faction, led by Edward Smith–Stanley, 14th Earl of Derby, and Benjamin Disraeli, survived to become the modern Conservative Party, whose members are commonly still referred to as Tories as they still often follow and promote the ideology of Toryism."
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