It really varies with the tournament. In one tournament I shoot in, primitive includes laminated bows, so long as no fiberglass is used. I suppose primitive would always include any self bow, so you would be pretty safe there. Wood arrows only, of course.
Tournaments also may have different rules within the traditional category, defining what is a longbow, for example. In a lot of tournaments, you have to shoot wood arrows in the longbow class. In some tournaments, longbows have to be one-piece, and D shaped when strung. In the recurve category, there are rules about stabilizers, sights, etc.