Age of sail- boat question

In naval stories and fiction of the age of sail, they often make ferences to a “jolly boat” a “barge” a “whaleboat” and such like of the ships boats. What’s the difference and why the names?

Well, different boats for different functions. And you have to call them something.

“Jolly” is of uncertain etymology. Probably from Danish, and maybe related to “Yawl”. Once sailors get their hands on some bit of foreign vocabulary, who knows will happen to it.

A whaleboat is kind of obvious – it’s what a whaler would launch to harpoon whales.

Then you have launches, barges, cutters, and pinnaces in more or less descending order of size. Although I seem to recall that “barge” is almost an honorary title – if it’s got the captain in it, it’s the captain’s barge, even if it’s a rowboat. Each of these can hold different number of oarsmen and most of them can mount one or more sails. Some of them are even big enough to mount small guns for landing or cutting out expeditions.

Don’t forget Gig. Captain’s Gig was popular.
The Hudson Sloop’s traditionally carried a Yawl Boat on winches at aft end.

Several entries on the Patrick O’Brian Discussion List discuss ship’s boats.