Is there a difference in the amount of ELO a player loses from resigning versus being checkmated?
If so - What is the difference in the calculation?
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No difference whatsoever. As with tournament results, ELO (or Glicko, or any other chess rating system) counts all losses the same, all draws the same, and all wins the same. Doesn't matter if you lose on time, resign, or get mated on the board --- nor whether it took 12 moves or 120. Likewise a draw is a draw, whether by agreement, repetition, stalemate (either side), or even the 50-move rule.
Elo rating system is widely used in non-chess competition too.
As for other rating systems (here's a comparison between Elo, Glicko, TrueSkill and ree, our free-to-use ranking algorithm), all wins count the same, even in sports/games with a score.
For multifaction rating system (e.g. for boardgames), calculations depend on all standings, so you need to correctly enter the full results, not just the winner (but scores still don't matter).
There are some game-specific implementations for including scores (or different winning condition) in rating algorithms, indeed (e.g. FiveThirtyEight for NFL).