Do you lose then same amount of Electrum and score when you quit and when you lose a game?
You are creating a false dichotomy. It's easy to understand why you asked this question, and a heavy percentage of people here have asked it before. To put it in perspective, that question is the same as asking, "Did that guy jump out of a 50th storey window and land on the pavement, or is he dead?"
To the computer, a quit *IS* a loss. The game code doesn't test for (quit OR loss). If you quit, you lost. Period. Full stop. End of conversation.
The computer makes no allowances or adjustments for
how you lost (deckout, 0 HP, quit, skipping an FG) or
how badly you lost (AI EM'd you, AI had 1 HP left). Want proof? Take a good look at the screen the next time you play in PvP1 or PvP2. The computer displays your reward for winning and your deduction for losing
before the duel begins. Therefore, quitting and losing CANNOT be two different things, except in human perception.
Although the computer does not give the same type of display for AI or Arena duels, the same rule applies. Neither type nor degree makes any difference. A loss is just a loss.