Thanks got itThere is no difference in that context.
Hold on does not mean "wait" it means "hold (i.e. keep) this telephone line open." and "on" indicates "continuing" - "hold on" dates back to the time when operators made the connections between phones.
Because "hang" is a stronger form of hold (i.e. to grip), "hang on" was a more emphatic form of "hold on." but currently hang on is considered informal and hold on is normal.
Thank you.Now it is clearThey mean the same thing, hang on is much more informal.
The problem might be that the second example is odd. "Hi, can I meet with David?" isn't what you'd expect to hear someone say as an introductory on the phone. "Hi, can I speak with David?", certainly.