here are some definition's for you out of the FAR's

Duty period means the period of elapsed time between reporting for an assignment involving flight time and release from that assignment by the certificate holder. The time is calculated using either Coordinated Universal Time or local time to reflect the total elapsed time.

If someone has not been called then they are not on duty,

but hmm then there is this nugget

Rest period means the period free of all responsibility for work or duty should the occasion arise.

wow looks like a contradiction to me