Etymology of "settee"?

I was reading Cochrane's Memoirs of a Fighting Captain when I came across this:-

However, at 3.00pm, as a large settee was running into the mole of Ciotat, we discharged two shots at her, which went over and fell into the town.

I was momentarily disconcerted by the notion of a seat, for two or more people, with a back and usually with arms sailing around the Mediterranean, pursued by Cochrane's frigate, but I persisted and turned up a vessel with a very long, sharp prow, carrying two or three masts with lateen sails, which makes rather more sense.

This leads me to wonder why a settee (the vessel) is so-called. Its name can't surely be connected with the item of furniture, can it?

They are probably unrelated. The ship came first in the 16th century and is from Italian saettia, is possibly from saetta, arrow. The furniture is from the 18th century and possibly from settle.

The OED has three definitions for settee. The first is the vessel, an earliest quotation from 1587, and is now historical:

Forms: 15 settea, 16 sattie, satty, satia, sett(y)e, 16–17 sattee, 17 cettee, saetia, setye, 16– settee.

Etymology: < Italian saettia (pronounced /-ˈtia/ ), ‘a very speedie pinnace’ (Florio 1598), of obscure origin, commonly viewed as < saetta arrow. Compare French scétie, setie, scitie.

A decked vessel, with a long sharp prow, carrying two or three masts with a kind of lateen sails, in use in the Mediterranean.

(The second, of unknown origin and rarely observed, is first quoted in 1688 and means "A double pinner for the head.")

The third, first quoted in 1716, is the furniture:

Etymology: perhaps a fanciful variation of settle n.1: see -ee suffix2.

A seat (for indoors) holding two or more persons, with a back and (usually) arms; occasionally also with divisions.