You could hear both of these on the phone. "Hold the line, please" "Hold on a minute, please" The first one is maybe more formal, but there is not much difference. They are just different ways of asking the person on the other end of the phone to wait a moment.

Yes, they both have the same meaning. "Hold the line, please" is more formal and could be used for business type phone calls. "Hold on a minute, please" is used in a more casual context.

Thank you very much.

Yes, it's the same in meaning.