"I'm sorry" and "my bad" mean the same thing, unless you're at a funeral.
Sorry vs. My Bad
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Explanation
Experiment
Explain Bear
Listen up, buttercup. "I'm sorry" is what you say when you accidentally step on someone's toe. "My bad" is what you mumble when you spill your juice box. But at a funeral, saying "my bad" after, say, dropping the casket? That ain't gonna fly. People are emotional and you need to be sensitive in a funeral.