These are games in the Checkers Family. Visit the wiki entry for more detailed information.
This family is characterized by players having identical pieces which capture by jumping.
According to the (mostly) reliable Wikipedia:
"English draughts (British English) or checkers (American English and Canadian English), also called American checkers or straight checkers is a form of the board game draughts. Unlike international draughts, it is played on an eight-by-eight squared board (with sixty-four total squares) with twelve pieces on each side. The pieces move and capture diagonally. They may only move forward until they reach the opposite end of the board, when they are crowned or kinged and may henceforth move and capture both backward and forward.
As in all draughts variants, English draughts is played by two people, on opposite sides of a playing board, alternating moves. Traditionally the pieces are either black, red, or white. The opponent's pieces are captured by jumping over them."
"International draughts (also called Polish draughts or international checkers) is a strategy board game for two players, one of the variants of draughts. It is played on a 10×10 board with alternatingly dark and light squares, of which only the 50 dark squares are used. The two players are at opposite sides, with 20 pieces each, light for one player and dark for the other. In conventional diagrams the board is displayed with the light pieces at the bottom and dark at the top and in this orientation the lower-left corner square must be dark."