The English terms for draughts are checker(s) and draughts
according to historians.

At the checker was a name that was also formerly used for the game of quek which is found in Jacob’s Well
(Anomiem, 1900).

Checkers is the name for draughts in the United States.

It still is a question if the term checker(s) was used for draughts before the 16th century. With all probability checker meant the
(checkered) chessboard of those times. The current term for draughts on 64 squares in Great Britain is draughts and this term is also found in the Middle Age. Nevertheless, it is still a question whether the term draughts referred to draughts at the time. It is much more likely that by the term draughts people meant alquerque of 12. French influences are clearly seen in the book by the Frenchman Pierre Erondelle (Erondell, 1605) and from the book of François Rabelais (Urquhart, 1653).
Did William Perkins (1966), who lived from 1558 until 1602, really refer to draughts in the 16th century? In Minsheu (1617a) we clearly see Spanish influences in their texts about draughts (Covarrubias, 1611).The first reference to draughts in a dictionary is not found before the end of the 16th century. (Florio, 1598).

For the full set of rules please do have a look at the World Checkers and Draughts Federation.