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1.Has six different pieces.
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Checkers pieces are men/pawns or kings. Chess has pawns, rooks, bishops, knights, queens, and kings.
2.Official American rules designate a board with 64 squares.
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They can be played on the same board, though checkers only uses the black squares.
3.The term “king me” is sometimes used.
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Chess has kings, but “king me” is only used in checkers when a pawn reaches the opposite end of the board and needs to become a king.
4.Pieces are captured by jumping over them.
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5.There is a move called “en passant.”
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En passant is a somewhat obscure chess move where a pawn can intercept an enemy pawn doing its two-square move.
6.Kings are allowed to move diagonally forwards or diagonally backwards.
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In chess, kings can move once in any direction. Kings in checkers always move diagonally, and what makes them a king is their ability to move in all four diagonals.
7.Also referred to as draughts in some places.
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Draughts is common in Britain. And sometimes checquers, I presume.
8.The game ends as a stalemate (a type of draw) if a player has no legal moves.
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If a player can’t move in checkers, they lose.
9.The game can end as a draw if there is no progress after several dozen moves.
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Chess becomes a draw in 50 moves with no progress. Checkers is drawn after 40 moves.
10.Taking an opponent’s piece is mandatory if it is possible.
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Checkers really needs this rule to prevent constant draws.
11.It is customary to say “check” when a king is threatened.
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12.White makes the opening move.
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White pieces play first in chess. Checkers usually has red and black pieces.
13.“Zugzwang” is often relevant to endgame strategy.
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Zugzwang is when any move worsens one’s position. Both games feature this concept.
14.Multiple pieces can be captured on a turn.
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In checkers, if a pawn captures a piece and lands on a square where it can capture another pawn, not only can it continue capturing pieces, it must.
15.Some pieces can move, or jump, “double” their normal number of squares in very specific circumstances.
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Pawns can move two spaces forward if they haven’t moved in the game yet. In checkers, capturing can result in double distance or much longer distances.
16.The top player has earned over $500,000 (USD) in yearly tournament winnings.
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Magnus Carlson made over 500K in 2021.
17.Is the older game.
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There is archaeological evidence of checkers in Ur circa 3000 BCE. Chess is much newer, from around 500 CE.
18.Very likely originated in an Asian country.
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Checkers was probably from Ur, in ancient Sumer, present-day Iraq. Chess originated in India.
19.The weakest piece can be upgraded into the strongest piece.
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Pawns in chess can upgrade to a queen, the strongest piece, by reaching the end of the board. Checkers has this mechanic, but pawns become kings.
20.Supercomputers have solved it
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Supercomputers solved the over 500 billion possible games of checkers from 1989-2007. Perfect play results in a draw. Chess has not been solved—AI can calculate board states, but the possible permutations in chess is around 10^126 and likely won’t be solved for a long, long time.
It actually varies by country, it seems. American checkers is the most widely played and is 8x8. Some countries play 10x10, and a few play 12x12. I’ll edit the question to make it fairer.