Unlocked or Off-line, refers to the same thing. All these are SIM Free GSM Phones that are sold without a connection or line and are not locked to any particular network. So you can be sure that the software that they have has not been interfered with. They also do not carry any logos or markings of a particular network. These phones can accept any SIM that is associated with a compatible frequency.
An "unlocked" cell phone will work for any service provider that supports the specific technology of the phone. A user switching service providers can keep a phone that is unlocked for any compatible service network. • GSM: AT&T Wireless, T-Mobile, and Cingular Wireless • TDMA: AT&T Wireless and Cingular Wireless • CDMA: Verizon Wireless and Sprint PCS