Simply put....
SCHRS provids a rating based on the boat, sail area, length, width, crew number, number of trapeses, daggers or not etc.
PY (US or UK) provides a rating based on the performance of the boat and the sailors who sail it.
consider a really difficult boat to sail. It will have one SCHRS rating.
Every year, as people get better at sailing it, the PY rating will change; this reflects the ability of the people sailing the boat, to sail the boat at it's petential.
Consider an old boat that is not sailed much. It will have one SCHRS rating, the PY tating will slowly get easier (slower) as less people sail it and so less people win stuff (the good guys usually sail in big fleets where the competition is).
So, after a while, the PY rating will become "easy" making the boat a bit of a bandit and as soon as a decent sailor "borrows" one, they clean up as the PY does not reflect the speed of the boat, it reflets the speed of the boat, and ALSO the speed of the people who sail the boat.
PY also does not allow rapid developemnt of classes as returns (Results) need to be gathered to create a rating.
SCHRS (or TEXEL), you just plug the data points into the rating engine and a rating pops out.