An arrest is the act of depriving a person of their liberty usually in relation to the purported investigation or prevention of crime and presenting the arrestee to a procedure as part of the criminal justice system.
Custody is the care, possession, and control of a thing or person. It is the retention, inspection, guarding, maintenance, or security of a thing within the immediate care and control of the person to whom it is committed. Thus custody is detention of a person by lawful authority or process.
Arrest is a short term event to be followed by Custody if approved of by a legal judicial authority.
Police Custody and Judicial Custody
Police custody literally means protection and care provided by the police while a person under judicial custody is under the protection and safety of a judge.
Police custody starts when a police officer arrests a suspect and reads him his rights while judicial custody happens when the judge orders that the suspect be put under this type of custody.
A suspect under police custody can be interrogated about the specific crime while this action is void under judicial custody. It can only be revoked when the judge orders it to be broken.
Police custody is the initial custody of a suspect. After a judge evaluates the case, the suspect can either have temporary freedom (by posting bail), judicial custody, or be taken again into police custody.