Bad-Rap-Bad-Rep | Commonly Confused Words

Bad rap

/bæd ræp/

A reputation that is unfairly negative or unjust criticism

This word has no synonyms

/ˈbæd rɛp/

A negative reputation or opinion someone or something has

Bad rap comes from rap sheet, which is a criminal record, associating rap with reputation faults.
Bad rep uses rep from reputation, as rep is a common shortening.
Both phrases imply negativity in terms of reputation, but they originate from slightly different contexts.
Rap is also used in music, indicating a different context than reputation.
Think of a rap sheet for bad rap and rep for reputation for bad rep.