carry vs adc
The role versus the function. ADC is a position, the marksman in bot lane; carry is what any player does when they win the game for the others. Every adc wants to carry, not every carry is an adc.
carry
Carrying is winning the game almost alone, because you are far stronger than the nine others. The word also names the champion expected to do it, whatever their lane: a fed mid carries, a top who split pushes carries. "protect me i carry" is a division of labour, not a boast.
open the page →adc
ADC, attack damage carry, is the name of the marksman's position in bot lane, the one who plays with the support. The word contains "carry" because historically it was the role that had to finish the game. Today "adc" means the position, even when the player in it has not carried anything.
open the page →Why they get mixed up
The word "carry" is inside "adc", and many conclude the marksman must be the team's carry. That is wrong in half of all games: the one who carries is the one who is fed, and it can be anyone. "peel for adc" asks to protect the position; "peel for the carry" asks to protect whoever is strong. It is not always the same person.