PRS, at the highest levels, is a political organisation (likewise the MU) and the temptations that affect the conduct of politicians (not, of course corruption as such, but the pressures to cut a coat according to cloth) affect both, and there is not reason to assume that the PRS definitions are strictly in accordance with the law. For example the "PRS rights" are not 100% coterminous with the legal aspects of copyright directed to pubic performance.

In practical terms - anon = PRS doesn't need to pay any author
Trad - PRS doesn't need to pay any author
Out of copyright - ditto
PD - ditto

So why would they distinguish?

It is right that copyright may in principle be lost by dedication.
There are however a number of principles of copyright law that apply to anonymous and psuedonymous works, and some affect the duration of copyright. The rules as to infringement of copyright for an arrangement are the same as for a wholly original work - reproduction does not need to be exact, merely substantial.

I think that concentration on the legal issue of whether there is copyright or not will not necessarily illuminate our search for a term for music or song that is rather like folk music or folk song but is not within the definition.
n organisation that cannot really be trusted,