The word escort is not a derogatory term. In most parts of the World it's a Legal Profession. Escorts are used for a variety of purposes and it's not sexual in nature most times.
Escort: An escort is hired for an extended period of time such as several hours and even days. An escort is expected to be attractive and presentable in public. They are often used to stand-in as a date for specific functions or entertainment for an evening. Escorts are paid for their time and their company and sexual favors are not included as part of their package. Some escorts will go as far as to offer a massaged or cuddle, but sexual favors would cross the line into illegal territory.
Prostitution: A prostitute is someone that has sex for money plain and simple. Some type of sexual favor will need to be provided, and the prostitute will require money for those services. The person generally just pays for the services rendered nothing more nothing less. Most prostitution agreements are for a very short period of time such as an hour.
There is a difference between the Two Terms. In most comments when mentioned without the proof is none other than speculating.