Essentially your are correct. Courtesans are woman who are able to display at least one and possibly many artistic attributes. It is most important that they can convey themselves in the social manner and conventions of the society in which they operate and be an adept conversationalist in a variety of subjects. While a sexual relationship is often expected from a generous patron or client the courtesan always has the final say in the arrangement. Emphasis is placed on the role of a companion, not as a prostitute. Very few Courtesans are paid in cash. Most western woman arrive at their status through a variety of means. Most that I know of would make an interesting novel but it is not very often talked about.
Cultures that have a tradition of courtesans such as Japan and China were trained from a very early age. Concubines were virtually owned whereas a courtesan such the Japanese Geisha had some freedom but not a lot as they were often indented to an "oka-san"
As in any ‘profession’ there is wide ranging disparities of what constitutes the difference between the prostitute and a courtesan. Western culture sees very little difference between the two. This has much to do with provisions within a marriage that neither partner should copulate outside of the marriage bed. This is not so a rigid requirement in other societies where the courtesan is accepted as a fully accepted member of society.
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