The following might be helpful designating the naval unit that Smith commanded in 1807-1808:

From The Memoirs of Sir Sidney Smith, Volumes I and II, by Edward Howard:

'On the 27th of October, 1807, [Smith] was appointed commander-in-chief of a squadron destined for particular service, the nature of which was not long in transpiring. The coast of Portugal was his destination...'-239.

'He was the more confirmed in this, as Lord Strangford promised his royal highness, on the faith of his sovereign, that the British squadron before the Tagus, or a sufficiently strong portion of it, commanded by Sir Sidney Smith, should be employed to protect his retreat from Lisbon, and insure the safety of his voyage to the Brazils.'-241.

'On the morning of the 29th, the Portuguese fleet sailed from the Tagus, with the Prince of Brazil and the royal family of Braganza on boards...This fleet consisted of eight sail of the line, four large frigates, several corvettes, brigs, and ships of war, besides twenty-five sail of merchantmen, forming in all a fleet of thirty-six sail. Whilst they passed through the British squadron, our ships fired each a salute of twenty-one guns, what was returned by an equal number.'

So, it appears that Sidney Smith commanded a squadron of the Royal Navy, and that the 'eight sail of the line, four large frigates, etc...' were Portuguese, not British. This is verified in a dispatch from Smith to the Honorable William Wellesley Pole, on 1 December 1807. (pages 247-248). Further, in the same dispatch, Smith refers to the assemblage of Portuguese men-of-war as a 'fleet.'

In a dispatch from Pole to Smith dated 27 October, stating, in part, that 'Whereas we have thought fit to appoint you commander-in-chief of a squadron of His Majesty's ships and vessels to be employed on a particular service...'

Further material, from primary source letters and dispatches in the volume continually refers to Smith's commands in 1807 and 1808 as squadrons, not fleets.

While part of the subject volume is written by the author, the primary source material in the volume, of letters and dispatches, definitely names Smith's commands as squadrons.