Game-key cards are different from regular game cards, because they don’t contain the full game data. Instead, the game-key card is your “key” to downloading the full game to your system via the internet.
Pay a premium for a physical copy of your game, and the cartridge may not contain the actual game. Only on Nintendo Switch 2.
It’s the other way around. You can download the same game in all of your consoles and actually play them at the same time. Something you can’t do with cartridges, because you can only play the game in the console where the cartridge is inserted. You’d need one cartridge per console to play the same game simultaneously. So digital games are objectively better for your scenario.
Can you download a game on the same account to two switches and play them at the same time?
Yes.