b vs back off
The destination. "b" means going back to base; "back off" means stepping back a few paces. One leaves the fight, the other repositions it.
b
"b" is short for back, and in chat it almost always means recall: I am going to base to buy and heal. It is an announcement, not an order. "b for items", "going b", "b after this wave". If someone tells you "b", they are telling you they are leaving, or advising you to leave.
open the page →back off
"back off" is an immediate movement order: step back, get out of range, do not take this fight. Nobody recalls on a "back off". It is used when a teammate walks too far forward, when a gank is coming, or when the fight is lost before it starts: "back off cant win".
Why they get mixed up
Both start with the same word, and both say to move back. But mixing them up is expensive: a player who recalls on a "back off" abandons a fight that only needed repositioning, and a player who steps back three paces on a "b" stays in lane with no health and no gold. When in doubt, "b" is a recall, "back off" never is.