Suspect is someone suspected of a crime, like they are not entirely sure they committed the crime. Culprit is someone definitely at fault for the crime

A suspect charged with a crime is the culprit

Culprit did the criminal activity Suspect I someone suspected of the crime

A suspect is a person who may or may not be responsible for an action. There are a suspect of wrong doing or under suspicion. For example "We do not know for sure if the suspect stole the shoes." Whereas culprit is definitely the wrong doer. It is know or proven that the culprit commit the action. For example "The culprit left evidence of that they committed the crime"

The suspect is under suspicion. The police think the suspect committed the crime but they are not sure. The culprit is the person who actually committed the crime. Sometimes the suspect is the culprit, but sometimes our suspicions are incorrect and the suspect is innocent.