Person To Person means that something is to take place directly between individuals.
For example in the old days of the phone service when you would tell the operator that you want to call someone they would sometimes ask if it's a person to person call.
And you would not be charged if the person does not answer the line on the other end.
That means that the call is from you to the other person on the line.
Such as you would be calling another individual at their home and speak to the person on the other end of the line.
If it was a person to business call then they would ask if it was a person to business call.
The person to business call would mean that you're calling a business to speak to someone at a company.
Although you're still speaking to a person at a business the rates for the calls were usually slightly higher to speak to a business than it would be to speak to a person at their home.
A person-to-person call is an operator-assisted call in which the calling party requests to speak to a specific party and not simply to anyone who answers.
The caller is not charged for the call unless the requested party is reached.
This method was popular when telephone calls were relatively expensive.