People who are healthy, without symptoms, but who might be infected can be quarantined, to protect people they might come in contact with. Quarantine comes from the Latin word for 40 days, which was how long people were watched, to see if they were infected with the plague in Medieval times.
Infected people, who are obviously contagious, are isolated. This procedure is also designed to protect people they might come in contact with.
Quarantine would often occur at home. Isolation is often accomplished in a hospital.