In my head I imagine they say something like...Hello, you have reached the answering service for ABC Company. Then what might they say?
      Answer1:They will say whatever the client wants them to say. Most do not advertise that it is an answering service.
      Answer2:The service will know what company a call will be coming in for and answer the phone accordingly. For companies that offer 24 hour service (doctors, plumbers, etc.) the answering service might screen the call before forwarding it. They might ask "is this an emergency", and then take necessary steps of forwarding the call or taking a message.