Sierra,
The difference is that a "private" concert is where the tickets are presold or usually not even printed. The promoter is replaced by a cooperative if you will or in some cases by one person with the financial means to pay the performer. The performer gets paid as usual except that there is no "markup" pocketed by the promoter. There is nothing sinister or elitist about it. We have all heard of some act or other being hired to play at some well-to-do person's wedding or bar mitzvah or just plain old party. And in the case of older performers it is often the only way they can get work. That is certainly not the case here but it would be fun if we could all get together and do it, don't you think?
Bill