Well knowing nothing about pelhams but looking at the photo's on the link page I'd say Rugby Pelhams have a third little ring on the bit shaft for a lip strap perhaps? And the loose ring show pelhams don't.
Thats a show pelham, rugbys have a little french link type thingy between the loose ring and the fixed part on the top side of the pelham. Rugbys usually have a thicker all round appearance than the show pelham which is far more dainty.