Rating system of the Royal Navy: 1st? 3rd? Rate? What is it?

The rating system of the Royal Navy and its predecessors was used by the British Royal Navy between the beginning of the 17th century and the middle of the 19th century to categorize​ sailing warships, initially classing them according to their assigned complement of men, and later according to the number of their carriage-mounted guns.

1st, 2nd, 3rd and 4th Rated Ship were considered ships of the line:

First Rate Ship - HMS Victory (1758)

Second Rate Ship - HMS Collingwood (1841)
Vanguard-class

Third Rate Ship - HMS Melville (1831)
Black Prince-class

Forth Rate Ship - HMS Leander (1814)
50-gun fourth rate

5th and 6th Rate Ships were considered Frigates:

Fifth Rate Ship - HMS Seahorse (1794)
Artois-class

Sixth Rate Ship - HMS Surprise / HMS Rose (Replica Example)

Unrated Ships
Sloops of War is a coined term to refer to cutters, brigs, and schooners fitted with less than 20 guns.

Bomb Vessel

The Batttle of Copenhagen by Nicolas Pocock. Bomb vessels can be seen in the bottom left, firing over the lines of British and Danish ships to hit the city in the background.