A person can be apprehended (usually by the police) if he suspect of being guilty of an arrestable offence. The way to apprehend a person is to arrest him.
Arrest can also be ordered by the court though warrants.
We can use "arrest" in any case since "apprehend" is too formal.
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apprehending a person means to catch a person suspected of a crime. Arresting a person means to formally charge the person with the alleged crime.