Just add onto this, the grace period is normally 10-20 days some registrar's leave the domain working during this time but some take it down. Then it goes into a "redemption period" for anywhere between 25 - 60 days. In the redemption period the registry tacks on a fee that is somewhere between $60 - $200 so the extra fee gets kicked up the chain.
Registrar: Who you registered the domain with
Registry: The company that owns the tld